Question

for h(x)=x^2-2x+7, compute, lim h(x)-h(1)/x-1
when x approach to 1

Answer 1

so...compute lim as x -->1 for ??? is that [h(x) - h(1)]/(x-1)?

Answer 2

\[\lim_{x \rightarrow 1} (x^2-2x+1)/(x-1) = \lim_{x \rightarrow 1} ((x-1)(x-1))/(x-1)\]

so, after factoring, and simplifying, you're left with...

Answer 3

lim x-->1 (x-1) = 0

Answer 4

what happened with 7?

Answer 5

h(x) = x^2-2x+7
h(1) = (1)^2-2(1)+7 = 6
h(x) - h(1) = x^-2x+7-6 = x^2-2x+1

Answer 6

cool