Can someone help me with rules of limits please! ;-;

Question

The question says to compute the limit and say which limit laws are used.

lim f(x) as x approaches 1 = 8

lim g(x) as x approaches 1 = 3

The problem is: lim cuberoot of [f(x)*g(x) + 3]

(as x approaches 1 of course)

I started with using the Root Rule and got confused if I'm allowed to do that or not because of the "+3".

Thank you so much in advance! :)

Answer 1

Okay, so you are given that:

lim f(x) = 8 & lim g(x) = 3

x→1 x→1

Thus,

lim ³√(f(x)g(x) + 3)

x→1

= ³√(lim ( f(x)g(x) + 3)

x→1

= ³√ (lim f(x)g(x) + lim 3)

x→1 x→1

*= ³√( 8*3 + 3)

= ³√ 27 = 3

*NOTE: lim 3 = 3 since it's just a constant. No matter what number you approach, your y - value always

x→1

wants to go to 3.

In other words: lim c = c (regardless of what number x is approaching)

x→a

Hope this helps.

Mr. K