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