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

##### 1 Answer

Nov 23, 2017

The limit equals

#### Explanation:

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:

Hopefully this helps!