Friday

August 22, 2014

August 22, 2014

Posted by **Tommy** on Thursday, April 26, 2012 at 10:33pm.

d) lim x_0+ (xe^(2x) + 1)^(5/x)

e) lim x_(Pi/2)+ (1 + sec3x)^(cot3x)

Thank you!

- Calculus 1 -
**Steve**, Friday, April 27, 2012 at 11:27amConsider (xe^(2x) + 1)^(5/x) → 1

^{oo}

Now, ln(x) is continuous for x>0, so use that to lower the complexity

ln(xe^(2x) + 1)^(5/x) = 5/x * ln(xe^(2x) + 1)

That's now oo * 0, which we can change to 0/0 by writing it as

ln(xe^(2x) + 1)/(x/5)

Now we can apply the Rule, to get

[e^2x (2x+1)/(e^2x+1)] / (1/5) = 5

Now, that means ln(limit) = 5, and the limit is e^5

Use the same trick to change

(1 + sec3x)^(cot3x) → oo^{0}

to get the limit = 1

**Related Questions**

calculus - Evaluate the following limits after identifying the indeterminate ...

Calculus - L'Hospital's Rule Lim(lnx)^(x-1) x->1+ This is what I did so far...

math - i need some serious help with limits in pre-calc. here are a few ...

Calculus - Find the following limits algebraically or explain why they don’t ...

Maths Calculus Derivatives & Limits - Using the definition of the derivative ...

Calculus - Below are the 5 problems which I had trouble in. I can't seem to get ...

Calculus - F(x)=|x-5| evaluate the following limits lim x->5- ( f(x)-f(5))/(x...

Calculus - Find the indicated limits. If the limit does not exist, so state, or ...

Calculus - Find the indicated limits. If the limit does not exist, so state, or ...

CALCULUS - Evaluate each of the following. (a) lim x->0(e^x)-1-x/ x^2 (b) lim...