Posted by **soumitra** on Friday, July 11, 2014 at 11:13am.

find the value

lim[(cos x)^1/2 -(cos x)^1/3]/(sinx)^1/2

x>0

- math -
**Steve**, Friday, July 11, 2014 at 11:29am
what tools do you have at your disposal? Have you learned l'Hospital's Rule yet? If so, that's what I'd use. The limit is the same as for the derivatives:

(1/2 cos(x)^-1/2 - 1/3 cos(x)^-2/3)(-sinx) / (1/2 sin(x)^-1/2 * cosx)

Take that sinx^-1/2 out of the bottom, and move it up top, and evaluate:

(1/2 - 1/3)(0)*0 / (1/2 * 1) = 0

## Answer This Question

## Related Questions

- Mathematics - Trigonometric Identities - Reiny - Mathematics - Trigonometric ...
- Math (trigonometric identities) - I was given 21 questions for homework and I ...
- Mathematics - Trigonometric Identities - Prove: sin^2x - sin^4x = cos^2x - cos^...
- Trig - prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= ...
- Trig - Simplify sin x cos^2x-sinx Here's my book's explanation which I don't ...
- pre-cal - Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos ...
- math - Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a...
- pre-calculus - which expression is equivalent to (sinx+1)(sinx-1)? A.) COS^2X B...
- Calculus - Q: If y=sinx/(1+tanx), find value of x not greater than pi, ...
- Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...

More Related Questions