Monday

March 2, 2015

March 2, 2015

Posted by **Joshua** on Tuesday, April 28, 2009 at 11:57pm.

Problem: limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x).

I did the problem out but I need help in seeing if its correct.

limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x)= (1-(1-x^2/2+x^4/4!-...))/(1+x-(1+x+x^2/2+x^3/3!+x^4/4!+...)=(x^2-x^4/4!+...)/(-x^2/2-x^3/3!-x^4/4!-...)=-11/17

- Calculus -
**Count Iblis**, Wednesday, April 29, 2009 at 8:50amIt is wrong. You also need to use the "Big O" notation. One denotes by

O(x^n) a term that for x to zero behaves as a constant times x^n. More rigorously, we say that some term T(x) is O(x^n) if and only if there exists a p and C such that

|T(x)| <= C |x^n| for all |x| < p

THen we can proceed as follows. We have:

1-cos(x) = 1/2 x^2 + O(x^4)

1 +x-exp(x) = -1/2 x^2 + O(x^3)

[1-cos(x)]/[1+x-exp(x)] =

-[1+O(x^2)]/[1+O(x)] =

-[1+O(x^2)][1+O(x)] =

-1 + O(x)

Limit of x to zero is then -1, because the O(x) tends to zero as it is less than x for x sufficiently close to zero.

**Answer this Question**

**Related Questions**

math - How to solve for delta using trig functions? i.e. cosine sine tangent ...

Calculus - Could someone please help me with these questions;I was having ...

Calc - I have a test soon.. and I really need to know how to do this problem.. ...

Calculus - What is the limit of this function as x approaches 0? cos(x) - 1 / x ...

calculus help again - if f'(x)=cos x and g'(x)=1 for all x, and if f(0)=g(0)=0, ...

Calculus - 1. Evaluate the function at the given numbers (correct to six ...

Calculus - Hi~ Thank you for your help! I was trying to work on a problem about ...

calculus - I'm not sure how to find the limit of this problem :S limit as x ->...

Differential Calculus - use the rule that says limit of (e^h - 1)/h = 1 as h ...

Differential Calculus - use the rule that says limit of (e^h - 1)/h = 1 as h ...