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If f(x) = {{:(-x-pi/2" , " x le - pi...

If `f(x) = {{:(-x-pi/2" , " x le - pi/2),(-cos x" , " -pi/2 lt x le 0",""then"),(x-1", "0lt x le 1),(ln x", "x gt 1):}`

A

f(x) is continous at `x=-pi/2`

B

`f(x)` is not differentiable at x=0

C

`f(x)` is differentiable at x=1

D

f(x) is differentiable at `x=-3/2`

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The correct Answer is:
A, B, C, D
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)
  1. The function f (x) = 1+ |sin x| is

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

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

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

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

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. If f(x) = {{:(-x-pi/2" , " x le - pi/2),(-cos x" , " -pi/2 lt ...

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  16. Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constan...

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  17. Let f be a real valued function defined on the interval [0,infty] by f...

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  18. Q. For every integer n, let an and bn be real numbers. Let function f:...

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  19. Let f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

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  20. Let f(x)={x^2 |cospi/x|, ,x !=0, x in R, x=0 then f is

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