Ex with lim: $lim_(x->4) ((sqrt(2x-7)-1)/(sqrt(x-3)-1))$ ?

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Answer 1 · 2017-11-23T21:47:35

The limit equals $2$

We have using L'hospitals:

$L = lim_(x->4) (2/(2sqrt(2x - 7)))/(1/(2sqrt(x - 3))$

$L = lim_(x->4) 2(sqrt(x - 3)/(sqrt(2x - 7)))$

We can now evaluate:

$L = 2(sqrt(4 - 3))/sqrt(2(4) - 7)$

$L = 2$

We confirm graphically:
enter image source here

Hopefully this helps!

Ex with lim: lim_(x->4) ((sqrt(2x-7)-1)/(sqrt(x-3)-1))lim_(x->4) ((sqrt(2x-7)-1)/(sqrt(x-3)-1)) ?