Question

Find limit as x approaches two of quantity x squared minus four divided by quantity x minus two. You must show your work or explain your work in words.

Answer 1

^ or if youre not sure how to derive yet, just factor the (x^2 - 4) and you would have (x-2)(x+2)/(x-2). then cross out the (x-2)s from top and bottom then plug 2 in, which gives you 4 :)

Answer 2

4

Explanation:

lim (x^2 - 4) / (x - 2)

x --> 2

When we plug x =2, we get

(2^2 - 4) / (2 - 2)

= (4 - 4)/(2 - 2)

= 0 /0

Which is undefined.

Now we have to use L'hospital rule. Which says we need to differentiate the numerator and the denominator and apply the limit.

When we differentiate x^2 -4, we get 2x

When we differentiate x -2, we get 1

lim 2x/1

x --> 2

Now apply, the limit x = 2

2(2)/1

= 4/1

= 4

Therefore, limit of this function is 4, when x tends to 2.

Hope you will understand the concept.

Thank you.