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

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1 Answer
May 23, 2018

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