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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" RR`

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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FULL MARKS-DIFFERENTIAL CALCULUS - DIFFERENTIABILITY AND METHODS OF DIFFERENTIATION-EXERCISE 5 (Choose the correct or the most suitable answer from the given four alternatives.)
  1. If y = cos ( sin x^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 + 5 log x)) is …........... .

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

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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= a sin theta and y =b cos theta, then (d^2 y)/(dx^2) is…............

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  8. The differential coefficient of log(m) x with respect to log(x) m 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 underset(x to a) (lim) (x f(a) - 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 underset( x to 0) (lim) ...

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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) = x |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)/(|x|)",", "elsewhere"):} ...

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  20. The number of points in RR in which the function f(x) = |x-1| + sin x ...

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