lim x tending to 0 (((cos x)^(1/2) - (cos x)^(1/3)) / (sin x)^2).Please solve this.
Debayan das , 7 Years ago
Grade 11
Differential Calculus> lim x tending to 0 (((cos x)^(1/2) - (cos...
4 Answers
Nandana
Last Activity: 7 Years ago
hi !
Ans : -1/6
Limx--> 0 √cosx – (cosx)1/3 0 form [LHospital’s rule]
sin2 x 0
Limx--> 0 [ ½ (√cosx)½ – 1/3 (cosx)-2/3 ] sinx = [ -½ (√cosx)-1 +1/3 (cosx)-2/3 ]
2 sin x cosx 2cosx
= -1/2 +1/3 = -1/6
Debayan das
Last Activity: 7 Years ago
The answer of this question is -1/12.Your answer is not correct .The answer of this question is -1/12.Your answer is not correct .
Nandana
Last Activity: 7 Years ago
hi !Sorry in my last answer I did a small mistake !Ans : -1/6 Limx--> 0 √cosx – (cosx)1/3 0 form [LHospital’s rule] sin2 x 0 Limx--> 0 [ ½ (√cosx)½ – 1/3 (cosx)-2/3 ] sinx = [ -½ (√cosx)-1 +1/3 (cosx)-2/3 ] 2 sin x cosx 2cosx Here is my mistake , = 1/2 (-1/2 +1/3) = -1/12 Now ok no ?It `s a calculation mistake , sorry & thank you very much for telling !
Nandana
Last Activity: 7 Years ago
hi ,
sorry for my mistake !
actually, what I did is correct but in the last step I did forget to multiply by half
here is what I ‘m talking about
Limx--> 0 √cosx – (cosx)1/3 0 form [LHospital’s rule]
sin2 x 0
Limx--> 0 [ ½ (√cosx)½ – 1/3 (cosx)-2/3 ] sinx = Limx--> 0 [ -½ (√cosx)-1 +1/3 (cosx)-2/3 ]
2 sin x cosx 2cosx
= ½ (1/3 -1/2) = -1/12
as your Answer !
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