Limit as x approaches zero of (sinx-(x^3/6)/x^5)

1. 👍 0
2. 👎 0
3. 👁 92
1. I assume you forgot the parentheses in the numerator,

Lim (sin(x)-(x^3/6))/x^5 as x->0

It would be easy to change sin(x) to a polynomial, the limits of which are easy to find.

If you expand sin(x) by Taylor's series, you'd get
sin(x)=x-x³/6+x^5/120...

So the expression becomes
(x-2x³/6+x^5/120-x^7/5040+...)/x^5 as x->0

which gives +∞

However, if the question had been

Lim (sin(x)-(x-x³/6))/x^5, the result would be 1/120

1. 👍 0
2. 👎 0

## Similar Questions

1. ### limits

what is the derivative of e^(3*ln(x^2)) i keep getting 6/x * e^(3*ln(x^2)) but that's not one of the multiple choice so am i doing something wront. also, what is the limit of (1-cosx)/(2*(sinx)^2) as x approaches zero. is the

asked by david on December 9, 2006
2. ### math

lim x->0 sinx secx / x use the fact that the limit as x approaches 1 of (sinx / x) = 1

asked by ag on September 20, 2011
3. ### Math

I've got quite a few problems. Please answer any of them in whole or in part. Thank you in advance. (For the record, you're not doing my homework; you're helping me understand it. These problems were not assigned.) (1). Determine

asked by Mark on March 3, 2009
4. ### Calculus Limits

Question: If lim(f(x)/x)=-5 as x approaches 0, then lim(x^2(f(-1/x^2))) as x approaches infinity is equal to (a) 5 (b) -5 (c) -infinity (d) 1/5 (e) none of these The answer key says (a) 5. So this is what I know: Since

asked by Anonymous on March 2, 2019
5. ### math

Find the limit of the function: (tanp)(x-1)/(tanq)(x-1) as x approaches 1. We're hinted at using the result that sinx/x = 1 as x approaches 0. Im not sure how we go abt doing this qs. thanks in advance

asked by sherry on December 31, 2008
1. ### Limits

What is the limit of (sinx)/x As x approaches 2?

asked by DuDu on September 11, 2012
2. ### Calculus

Determine the limit of the trigonometric function: Limit as x approaches pi/4 of (1-tanx)/(sinx-cosx) I need step by step help using the special trignometric limits theorem.

asked by Kayla on September 26, 2012
3. ### calculus

what is the limit of (1-tanx)/(sinx-cosx) as x approaches pi/4?

asked by Harv on September 28, 2009
4. ### calc

Using L'Hospital's Rule, find, the limit as x approaches 0 of x^(sinx)

asked by Laura on February 26, 2009
5. ### Calculus

Limit as x approaches 0 of x(1-cosx)/t-sinx. Confused on how to get this answer.

asked by Tim on April 21, 2014

More Similar Questions