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If f(x) = {{:({x+(1)/(3)}[sin pi x]",",0...

If `f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(3))",",1 le x le 2):}`, where [.] and {.} denotes greatest integerd and fractional part of x respectively, then the number of points, which is not differentiable, is

A

3

B

4

C

5

D

6

Text Solution

Verified by Experts

The correct Answer is:
C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (Single Option Correct Type Questions)
  1. If f(x) = {{:([cos pi x]",",x le 1),(2{x}-1",",x gt 1):}, where [.] an...

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  2. If f(x) = {{:(x - 3",",x lt 0),(x^(2) - 3x + 2",",x ge 0):}, then g(x)...

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  3. If f(x) = {{:({x+(1)/(3)}[sin pi x]",",0 le x lt 1),([2x]sgn(x - (4)/(...

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  4. Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for...

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  5. Let f(x+y) = f(x) + f(y) - 2xy - 1 for all x and y. If f'(0) exists an...

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  6. A derivable function f : R^(+) rarr R satisfies the condition f(x) - f...

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  7. If (d(f(x)))/(dx) = e^(-x) f(x) + e^(x) f(-x), then f(x) is, (given f(...

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  8. Let f : (0, oo) rarr R be a continuous function such that f(x) = int(0...

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  9. For let h(x)={1/q if x=p/q and 0 if x is irrational where p & q ...

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  10. Let f(x) = (g(x))/(h(x)), where g and h are continuous functions on th...

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  11. f(x)=(cosx-sin2x)/((pi-2x)^2);g(x)=(e^(-cosx)-1)/(8x-4pi)

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  12. If f(x) = (x-e^(x) + cos 2x)/(x^(2)), x ne 0 is continuous at x = 0, t...

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  13. Consider the function f(x) = [{:(x{x}+1",","if",0 le x lt 1),(2-{x}","...

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  14. Let f(x) = [{:((2^(x)+2^(3-x) - 6)/(sqrt(2^(-x))-2^(1-x))",","if",x gt...

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  15. Let [x] denote the integral part of x in R and g(x) = x- [x]. Let f(x...

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  16. Let f be a differentiable function on the open interval(a, b). Which o...

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  17. Number of points where the function f(x)=(x^2-1)|x^2-x-2| + sin(|x|) i...

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  18. Consider function f: R - {-1,1}-> R. f(x)=x/[1-|x|] Then the incorrect...

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  19. If the functions f : R -> R and g : R -> R are such that f(x) is conti...

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  20. The total number of points of non-differentiability of f(x) = min[|sin...

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