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lim(x to pi//4)(1- tan x)/(1-sqrt(2) sin...

`lim_(x to pi//4)(1- tan x)/(1-sqrt(2) sin x)` equals:

A

`1/sqrt(2)`

B

`1/2`

C

`1/(2sqrt(2))`

D

1

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The correct Answer is:
D
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)
  1. lim(x to pi//4) (sqrt(2)cos x-1)/(cot x-1) equals

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  2. lim(x to pi//4)(1- tan x)/(1-sqrt(2) sin x) equals:

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  3. lim(x to 0) (sin 2x)/x is equal to:

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  4. The function f defined as f(x) = (sin x^(2))//x for x ne 0 and f(0)=0 ...

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  5. For a real number y, let [y] denotes the greatest integer less than o...

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  6. There exists a function f(x) satisfying f{0} =1, f'{0} =-1, f(x) gt ...

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  7. The function f (x) = 1+ |sin x| is

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  8. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

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  9. The following functions are continuous on (0, pi)

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  10. If f (x) = 1/2 x - 1, then on the interval [0, pi]

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  11. If f(x) = 3x-5, then f^(-1) (x)

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  12. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

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  13. Show that the underset(xto2)lim((sqrt(1-cos{2(x-2)}))/(x-2)) doesnot e...

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  14. Let f: R to R be a positive increasing function with lim(x to infty) (...

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  15. If underset(x to infty)lim((x^(2)+x+1)/(x+1)-ax -b)=4 then

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  16. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

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  17. Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f...

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  18. If f: R to R is a function defined by f(x) = [x] cos((2...

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  19. Let L= lim(x to 0)(a- sqrt(a^(2)-x^(2))-x^(2)/4)/x^(4), a gt 0. If L i...

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  20. Let f: R to R be a function such that f(x+y) = f(x) + f(y) AA x, y in...

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