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underset(xto0)lim((1+tanx)/(1+sinx))^(co...

`underset(xto0)lim((1+tanx)/(1+sinx))^(cosecx)` is equal to

A

`-1`

B

e

C

1

D

`e^(-1) `

Text Solution

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The correct Answer is:
C
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AAKASH INSTITUTE ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Section -B
  1. lim(x->0)(1/(x^2)-1/(tan^2x))

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  2. lim(x to oo) ((x-3)/(x+2))^x is equal to :

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  3. underset(xto0)lim((1+tanx)/(1+sinx))^(cosecx) is equal to

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  4. lim(x->0)((4^x+9^x)/2)^(1/x)

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  5. If underset (xrarr0)"lim"(cosx+asinbx)^(1/x)=e^(2) then the possible v...

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  6. underset(x to 0)(Lt) (sqrt(1 - cos 2 x))/(sqrt(2)x) =

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  7. lim(x to 2^+) (([x]^(3))/(3) - [(x)/(3)]^(3)) is where [x] represents ...

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  8. The value of lim(x to 0) ((4^(x) - 1)^(3))/("sin"(x)/(4) log (1 + (x^...

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  9. If f(x)= {:{((x^(2) + 3x+p)/(2(x^(2)-1)) , xne 1),(5/4, x = 1):} is co...

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  10. In order that the function f(x)=(x+1)^(cotx) is continuous at x = 0, f...

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  11. The number of points at which the function f(x) = 1/ (log |2x|) is di...

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  12. If f(x)={:{(xe^(-(1/(|x|) + 1/x)), x ne 0),(0 , x =0 ):} then f(x) is

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  13. The set of points where f(x)=x/(1+|x|) is differentiable is

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  14. The function |x^2 - 3x+2| + cos |x| is not differentiableat x=

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  15. At x = 0 , the function y = e^(-|x|) is

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  16. Let f(x) = lambda + mu|x|+nu|x|^2, where lambda,mu, nu in R, then f'(0...

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  17. If {x} denotes the fractional part of x, then underset(x to 0)(lim) ({...

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  18. Let f(x) = [x] , g(x)= |x| and f{g(x)} = h(x) ,where [.] is the gre...

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  19. A function f is defined by f(x^(2) ) = x^(3) AA x gt 0 then f(4) equ...

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  20. If 3sin(x y)+4cos(x y)=5 , then (dy)/(dx)= (a) y/x (b) (3sin(x y)+4...

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