Question

HELP Use the definition of continuity and the properties of limits to show that’s the function…

Answer 1

Answer with Step-by-step explanation:

We are given that

$g(x)=(x^2-3x-10)(x^2+2x^2-5x+4)$

x=-1

Using property of limit

$\lim_{x\rightarrow -1}g(x)=\lim_{x\rightarrow -1}(x^2-3x-10)(3x^2-5x+4)$

=$(1+3-10)(3+5+4)$

=$(-6)(12)$

=$-72$

$g(-1)=(1+3-10)(1+2+5+4)$

$g(-1)=(-6)(12)=-72$

$\lim_{x\rightarrow -1}g(x)=g(-1)$

Hence, the function is continuous at x=-1