What is the limit of $7/(4(x-1)^2)$ as x approaches 1?

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Answer 1 · 2018-04-16T16:58:04

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First, rewrite this as $lim_(x->1) 7/(4(x-1)^2$

now factor $(x-1)^2$ = $(x-1)(x-1)$ = $x^2-2x+1$

$\frac{7}{4x^2-2x+1}$

now substitute x $->$ 1

$\frac{7}{4(1)^2 -2(1)+1$

$7/3$

$therefore lim_(x->1) 7/(4(x-1)^2) = 7/6$

What is the limit of 7/(4(x-1)^2)7/(4(x-1)^2) as x approaches 1?