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If f(x) = {{:(2a-x, "for",-a lt x lt a),...

If `f(x) = {{:(2a-x, "for",-a lt x lt a),(3x-2a ,"for", x ge a):}`, then which one of the following is true?

A

f(x) is not differentiable at x=a

B

f(x) is discontinuous at x=a

C

f(x) is continuous for all x in R

D

f(x) is differentiable for all `x ge a`

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Verified by Experts

The correct Answer is:
A
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SURA PUBLICATION-DIFFERENTIAL CALCUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION-EXERCISE 10.5
  1. If y=cos(sinx^(2)), " then " (dy)/(dx) " at " x=sqrt(pi/2) is

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  2. If y=mx+c " and " f(0)=f'(0)=1, " then " f(2) is

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  3. If f(x)=xtan^(-1)x, then f'(1) is

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  4. d/dx(e^(x+5logx))

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  5. If the derivative of (ax-5)e^(3x) at x=0 is -13, then the value of a i...

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  6. x=(1-t^(2))/(1+t^(2)), y=(2t)/(1+t^(2)) " then " (dy)/(dx) is

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  7. If x=asintheta " and " y=bcostheta, " then " (d^(2)y)/(dx^(2)) is

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  8. The differential coefficient of log(10)x with respect to log(x)10 is

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  9. If f(x)=x+2, " then " f'(f(x)) at x=4 is

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  10. If y=(1-x)^(2)/x^(2), " then " (dy)/(dx)= is

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  11. If pv = 81, then (dp)/(dv) at v=9 is

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  12. If f(x) = {{:(x-5, "if" , x le 1),(4x^2-9, "if", 1 lt x lt 2),(3x+4 ,"...

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  13. It is given that f'(a) exists,then lim(xrarra)(xf(a) - af(x))/(x - a) ...

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  14. If f(x) = {{:(x+1, "when" , x lt 2),(2x-1, "when" ,x ge 2):}, then f'(...

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  15. If g(x) = (x^(2)+2x+3), f(x) and f(0)=5 and lim(xrarr0)(f(x)-5)/x = 4 ...

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  16. If f(x)={{:(x+2, -1 lt x lt 3), (5, x=3), (8-x, x gt 3):}, then at x=3...

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  17. The derivative of f(x)=xabs(x) at x=-3 is

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  18. If f(x) = {{:(2a-x, "for",-a lt x lt a),(3x-2a ,"for", x ge a):}, then...

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  19. If f(x)={{:(ax^(2)-b",", -1 lt x lt 1), (1/abs(x)",", "elsewhere"):} i...

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  20. The number of points in R in which the function f(x)=abs(x-1)+abs(x+3)...

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