Question

(x²-x+

Answer 1

Sorry to disappoint, but none of these answers are correct. All three limits are equal to 7.

Compute the one-sided limits:

$\displaystyle\lim_{x\to2^-}h(x)=\lim_{x\to2}(x^2-x+5)=2^2-2+5=7$

$\displaystyle\lim_{x\to2^+}h(x)=\lim_{x\to2}(x^3-1)=2^3-1=7$

Both the one-sided limits agree, so the two-sided limit has the same value,

$\displaystyle\lim_{x\to2}h(x)=7$