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How do you find the limit of #(1/(x+4)-(1/4))/(x)# as #x->0#?

Answer 1

Christopher Allers

#-1/16#

Find a common denominator within the fractions of the numerator:

#lim_(xrarr0)(1/(x+4)-1/4)/x=lim_(xrarr0)(4/(4(x+4))-(x+4)/(4(x+4)))/x#

#=lim_(xrarr0)(4-(x+4))/(x(4(x+4)))=lim_(xrarr0)(-x)/(4x(x+4))#

#=lim_(xrarr0)(-1)/(4(x+4))#

Now the limit can be evaluated since the #x# has been removed from the denominator:

#=(-1)/(4(0+4))=-1/16#

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Answer 2

Elijah Abram

To find the limit of the expression (1/(x+4)-(1/4))/(x) as x approaches 0, we can simplify the expression first.

First, let's find a common denominator for the two fractions in the numerator. The common denominator is 4(x+4).

Next, we can combine the fractions in the numerator by subtracting them. This gives us ((4- (x+4))/(4(x+4)))/(x).

Simplifying further, we have (-x)/(4(x+4))/(x).

Now, we can simplify the expression by canceling out the x terms in the numerator and denominator. This leaves us with -1/(4(x+4)).

Finally, we can take the limit as x approaches 0. Plugging in 0 for x, we get -1/(4(0+4)) = -1/16.

Therefore, the limit of (1/(x+4)-(1/4))/(x) as x approaches 0 is -1/16.

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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.

How do you find the limit of #(1/(x+4)-(1/4))/(x)# as #x-&gt;0#?

How do you find the limit of #(1/(x+4)-(1/4))/(x)# as #x->0#?