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How do you evaluate # (x-7)/(x^2-49)# as x approaches 7?

Answer 1

Samantha Adkison

#lim_(x->7) (x-7)/(x^2-49)# can be rewritten as

#lim_(x->7) cancel((x-7))/(cancel((x-7))(x+7)) = lim_(x->7) (1)/(x+7)=1/14#

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Answer 2

Ezekiel Alexander

To evaluate (x-7)/(x^2-49) as x approaches 7, we substitute 7 for x in the expression. This gives us (7-7)/(7^2-49), which simplifies to 0/0. However, 0/0 is an indeterminate form, meaning further evaluation is needed. To proceed, we can factor the denominator as (x+7)(x-7). Canceling out the common factor of (x-7), we are left with 1/(x+7). Substituting 7 for x in this expression gives us 1/(7+7), which simplifies to 1/14. Therefore, as x approaches 7, the value of (x-7)/(x^2-49) approaches 1/14.

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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.