Evaluate the Limit

[jordangro]

Need help evaluating the limit:

lim [ cos(4x)-1 ] / [ (5th-rt(1+3x) - 1) * sin(2x) ]
x-->0

I know I have to use l'hopital's rule. I tried, but I get stuck in the second step with 0/some number. Any suggestions?

 

[stapel]

Need help evaluating the limit:

lim [ cos(4x)-1 ] / [ (5th-rt(1+3x) - 1) * sin(2x) ]
x-->0

I am reading the above as meaning the following:

. . . . .\(\displaystyle \displaystyle{ \lim_{x\, \rightarrow\, 0}\, \frac{\cos(4x)\, -\, 1}{\left(\sqrt[5]{1\, +\, 3x\,}\, -\, 1\right)\sin(2x)} }\)

If this is wrong, kindly please reply with corrections. Otherwise...

I know I have to use l'hopital's rule. I tried, but I get stuck in the second step with 0/some number.

Please reply showing what you did and what you got. Thank you!

 

[ameri]

Hi
If anyone could tell me how should I write equations that would be great.
Here is the limit after the L'hospital:
lim(-[4sin(4x)]/[2(5th-rt(1+3x)-1)cos(2x)+([3sin(2x)]/[5((1+3x)^(4/5))])]) x-->0