How do you evaluate the limit #(x+3)/(2x^2+2x+1)# as x approaches #3#?

Answer 1

By substitution.

If #x# is close to #3#, the #x+3# is close to #6# and
#2x^2+2x+1# is close to #2(3)^3+2(3)+1 = 25#.
So the quotient is close to #6/25#.
#lim_(xrarr3) (x+3)/(2x^2+2x+1) = 6/25#
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Answer 2

To evaluate the limit (x+3)/(2x^2+2x+1) as x approaches 3, we substitute 3 for x in the expression. This gives us (3+3)/(2(3)^2+2(3)+1). Simplifying further, we have 6/(18+6+1). Continuing to simplify, we get 6/25. Therefore, the limit is 6/25 as x approaches 3.

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Answer from HIX Tutor

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.

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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