Thread: Calculas- limits

Apply limit laws to evaluate or show that the limit does not exist.

lim Cos (π + ∆ x) +1
∆x -> 0 ∆x


I started like this but It didnt go anywhere:

lim Cos (π + ∆ x) +1 . Cos (π + ∆ x) -1 = lim Cos (π + ∆ x)^2 -1
∆x -> 0 ∆x Cos (π + ∆ x) -1 ∆x -> 0 ∆x(Cos(π + ∆ x) -1

please help me thanks[IMG]file:///C:/DOCUME%7E1/Shayan/LOCALS%7E1/Temp/moz-screenshot-5.jpg[/IMG][IMG]file:///C:/DOCUME%7E1/Shayan/LOCALS%7E1/Temp/moz-screenshot-6.jpg[/IMG]

Hi, meme22!

Originally Posted by meme22

Apply limit laws to evaluate or show that the limit does not exist.

lim Cos (π + ∆ x) +1
∆x -> 0 ∆x


I started like this but It didnt go anywhere:

lim Cos (π + ∆ x) +1 . Cos (π + ∆ x) -1 = lim Cos (π + ∆ x)^2 -1
∆x -> 0 ∆x Cos (π + ∆ x) -1 ∆x -> 0 ∆x(Cos(π + ∆ x) -1

I assume this is the problem you are trying to solve:



Is that right?

First of all, you can easily see what this limit should be if you observe that



.

So, we should suspect the limit to be zero. Now, to solve it using the properties of limits, here are some hints:

1. Use the fact that to rewrite the numerator

2. Make sure that you are familiar with this special limit:



Does that help?

Yes, thank you I figured it out