# How do you express as a partial fraction #1/(s^2 +1)^2#?

The expression cannot be further decomposed.

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[ \frac{1}{(s^2 + 1)^To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factorTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

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[ \frac{1}{(s^2 + 1)^2}To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominatorTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} =To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator asTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \fracTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as (To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (sTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{ATo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 +To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1}To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \fracTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{BTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 =To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(sTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (sTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 +To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(sTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2}To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} \To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

ThenTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then,To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1)To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constantsTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since theTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants (To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominatorTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( ATo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator isTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A \To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeatedTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) andTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated,To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and (To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, weTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B )To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we useTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying bothTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use theTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides byTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the followingTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following formTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 +To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(sTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 \To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 )To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2} = \To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 ) and equating coefficientsTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2} = \fracTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 ) and equating coefficients of likeTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2} = \frac{To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 ) and equating coefficients of like termsTo express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2} = \frac{AsTo express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 ) and equating coefficients of like terms.To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2} = \frac{As +To express ( \frac{1}{(s^2 + 1)^2} ) as partial fractions, you would write it as:

[ \frac{1}{(s^2 + 1)^2} = \frac{A}{s^2 + 1} + \frac{B}{(s^2 + 1)^2} ]

Then, you solve for the constants ( A ) and ( B ) by multiplying both sides by ( (s^2 + 1)^2 ) and equating coefficients of like terms.To express ( \frac{1}{(s^2 +1)^2} ) as a partial fraction, we first factor the denominator as ( (s^2 +1)^2 = (s^2 +1)(s^2 +1) ). Since the denominator is repeated, we use the following form for the partial fractions:

[ \frac{1}{(s^2 +1)^2} = \frac{As + B}{s^2 +1} + \frac{Cs + D}{(s^2 +1)^2} ]

Next, we find the values of ( A ), ( B ), ( C ), and ( D ) by equating coefficients:

[ 1 = (As + B)(s^2 +1) + (Cs + D) ]

Expanding and matching coefficients, we get:

[ 1 = As^3 + As + Bs^2 + B + Cs + D ]

Matching coefficients:

[ A = 0 ] [ B + C = 0 ] [ A + D = 1 ] [ B = 0 ]

From the first and fourth equations, we have ( A = 0 ) and ( B = 0 ), respectively.

From the second equation, ( B + C = 0 ), so ( C = -B = 0 ).

From the third equation, ( A + D = 1 ), so ( D = 1 ).

Therefore, the partial fraction decomposition of ( \frac{1}{(s^2 +1)^2} ) is ( \frac{1}{(s^2 +1)^2} = \frac{1}{s^2 +1} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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