Question

Answer the following questions: Please refer to the questions in the image: Thank you?

Answer 1

a) `color(blue)[lim_(xrarr3^-)(x+3)/(x^2-9)=-oo]`
b)`color(red)[lim_(xrarr-4^+)(9x)/(16-x^2)=oo`

Explanation:

i will solve question 1

a) `color(blue)[lim_(xrarr3^-)(x+3)/(x^2-9)]`

take a number from left of 3 like 2.9

now offset it in the limit `lim_(xrarr3^-)(x+3)/(x^2-9)`

if the sign of the limit equal `-` that mean the value of limit equal `-oo` ,but if the sign of the limit equal `+` that mean the limit equal `+oo`

`lim_(xrarr3^-)(x+3)/(x^2-9)=(2.9+3)/(8.41-9)=+/(-)=-`

`lim_(xrarr3^-)(x+3)/(x^2-9)=-oo`

b)`color(red)[lim_(xrarr-4^+)(9x)/(16-x^2)`

take a number from right of -4 like -4.1

offset it in the limit `lim_(xrarr-4^+)(9x)/(16-x^2)`

we will get

`lim_(xrarr-4^+)(9x)/(16-x^2)=(-36.9)/(16-16.81)=-/(-)=+`

`lim_(xrarr-4^+)(9x)/(16-x^2)=oo`