Question

Evaluate the following limit: lim x->2 (x^7-2^7)/(x^2-2^2)

Answer 1

lim x->2 (x^7-2^7)/(x^2-2^2)
Substitute your values in.

(2^7-2^7)/(2^2-2^2) = 0/0
This means there is a limit and we need to factorise in order to get the limit

lim x->2 = (x-2) (x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64)/(x-2)(x+2)
lim x->2 = (x^6+2 x^5+4 x^4+8 x^3+16 x^2+32 x+64)/(x+2)
lim x->2 = (sub in your x=2 values, I used a calculator)
lim x->2 = 112

Answer 2

Thanks! I had figured out that I needed to factorise, but I didn't know how. Now I get it!