Saturday

December 20, 2014

December 20, 2014

Posted by **Emily** on Monday, January 30, 2012 at 11:52pm.

lim tan(pi(x/4)) as x-> -7

lim (x^2 - x^3(cos(1/x))/3x^2 as x-> 0

I know the answer to the first problem is 1 and to the second problem it's 1/3 but I'm not sure how to get these answers. Any help is greatly appreciated! :)

- Calculus I -
**Reiny**, Tuesday, January 31, 2012 at 12:40amThe first step in any limit question is to actually substitute the approach value into the expression.

If you get a real number as an answer, that is it, you are done

so Lim tan(πx/4) as x ---> -7

= lim tan(-7π/4)

= 1

in lim (x^2 - x^3(cos(1/x)/(3x^2) as x ---> 0

= lim (1-xcos(1/x))/3

no matter what cos(1/x) is , xcos(1/x) ---> 0 as x-->0

(multiplying anything by zero, is zero!)

so lim (1-xcos(1/x))/3

= (1 - 0)/3 = 1/3

- Calculus I -
**Emily**, Tuesday, January 31, 2012 at 10:53amReading these answers makes a whole lot more sense after a night's sleep, haha. Thank you so much!

**Answer this Question**

**Related Questions**

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

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

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

CALCULUS - need help! - Determine the limit of the trigonometric function (if it...

calculus - The limit represents the derivative of some function f at some number...

Calculus..more help! - I have a question relating to limits that I solved lim(x...

Limits - Let lim f(x) =16 as x->4 and lim g(x) =8 as x->4 Use the limit ...

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 ...

Calc. Limits - Are these correct? lim x->0 (x)/(sqrt(x^2+4) - 2) I get 4/0...