math
posted by soumitra .
find the value
lim[(cos x)^1/2 (cos x)^1/3]/(sinx)^1/2
x>0

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
Respond to this Question
Similar Questions

Trig
prove the identity (sinX)^6 +(cosX)^6= 1  3(sinX)^2 (cosX)^2 sinX^6= sinx^2 ^3 = (1cosX^2)^3 = (12CosX^2 + cos^4) (1cosX^2) then multiply that out 12CosX^2 + cos^4  cosX^2 + 2cos^4 cos^6 add that on the left to the cos^6, and … 
math b
if sinx=(4/5), where 0 degrees<x<90 degrees, find the value of cos (x+180) 25+25+100+n=250 since x is in the first quadrant, then x+180ยบ is in the third quadrant, and cos(x+180) = =cos x You should recognize the 3,4,5 rightangled … 
precal
Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x 48 
Mathematics  Trigonometric Identities
Prove: sin^2x  sin^4x = cos^2x  cos^4x What I have, LS = (sinx  sin^2x) (sinx + sin^2x) = (sinx  1 cos^2x) (sinx + 1  cos^2x) = sin^2x + sinx  sinx  cos^2xsinx  cos^2xsinx  1  1 + cos^4x = sin^2x  2cos^2xsinx  2 + cos^4x … 
Mathematics  Trigonometric Identities  Reiny
Mathematics  Trigonometric Identities  Reiny, Friday, November 9, 2007 at 10:30pm (sinx  1 cos^2x) (sinx + 1  cos^2x) should have been (sinx  1 + cos^2x) (sinx + 1  cos^2x) and then the next line should be sin^2x + sinx  cos^2xsinx … 
Trig
Simplify sin x cos^2xsinx Here's my book's explanation which I don't totally follow sin x cos^2xsinx=sinx(cos^2x1) =sinx(1cos^2x) =sinx(sin^2x) (Where does sine come from and what happend to cosine? 
math
Determine exact value of cos(cos^1(19 pi)). is this the cos (a+b)= cos a cos b sina sin b? 
Math (trigonometric identities)
I was given 21 questions for homework and I can't get the last few no matter how hard and how many times I try. 17. Sinx1/sinx+1 = cos^2x/(sinx+1)^2 18. Sin^4x + 2sin^2xcos^2x + cos^4x = 1 19. 4/cos^2x  5 = 4tan^2x  1 20. Cosx … 
precalculus
which expression is equivalent to (sinx+1)(sinx1)? 
Math
I need help solving for all solutions for this problem: cos 2x+ sin x= 0 I substituted cos 2x for cos^2xsin^2x So it became cos^2(x)sin^2(x) +sinx=0 Then i did 1sin^2(x)sin^2(x)+sinx=0 = 12sin^2(x)+sinx=0 = sinx(2sinx+1)=1 What …