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If f(x)=int(-1)^(x)|t|dt ,x>=-1 then...

If f(x)=`int_(-1)^(x)|t|dt ,x>=-1 ` then

A

f and f' are continuous for `x+1 gt 0`

B

f is continuous but f' is not continuous for `x + 1 gt 0`

C

f and f' are not continuous at x = 0

D

f is continuous at x = 0 but f' is not so

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The correct Answer is:
A
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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (2) (MULTIPLE CHOICE QUESTIONS)
  1. The value of k which makes f(x) = {{:(sin(1//x), x ne 0),(k, x =0):}, ...

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  2. f(x) = {{:(-1, x lt -1),(-x, -1 le x le 1),(1, x gt 1):} is continous

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  3. If f(x)=int(-1)^(x)|t|dt ,x>=-1 then

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

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  5. Given the function f(x) = 1/(1-x). The points of discontinuity of the ...

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  6. If f(x) is defined by: f(x) = {{:((|x^(2)-x|)/(x^(2)-x), (x ne 0,1)),(...

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  7. Let f(x) =|x| + |x-1|, then

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  8. The function f(x)=|x|+|x-1|,is

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  9. Let f(x) = {{:((x^(4) -5x^(2)+4)/(|(x-1)(x-2)|), (x ne 1,2)),(6, x=1),...

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  10. Let f(x) =x-|x-x^(2)|, x in [-1,1].Then the number of points at which ...

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  11. The function f(x) =[x]^(2) -[x^(2)] (where [y] is thegreatest integer ...

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  12. On the interval [-2,2] the function: f(x) = {{:((x+1)e^(-{1/|x|+1/x}...

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  13. Let f(x) = {{:(int(0)^(x) {5+|1-t|dt}, if x gt 2),(5x+1, if x le 2):},...

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  14. The function f(x) =[x] cos{(2x-1)//2} pi denotes the greatest integer...

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  15. The number of points where f(x) =[sin x + cos x] (where [.] denotes th...

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  16. Let f: R to R be any function. Define g : R to R by g(x) = | f(x)|, A...

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  17. If f(x) ={{:(x(e)^(-[1/|x|+1/x]), x ne 0),(0, x=0):}, then f(x) is:

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

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  19. If f(x) = {{:(1, x lt 0),(1 + sinx, 0 le x lt pi//2):} Then at x=0, t...

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

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