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Let f be a function defined on [0,oo) by...

Let f be a function defined on `[0,oo)` by
`f(x)={{:(0,,x=0),((x+a//sqrt(2))(1//sqrt(2)),,0lt x le a),((x//2+a)(1//sqrt(2)),,x ge a):}` then

A

f'(x) is discontinuous at x = 0, a

B

f is a continuous function

C

f is discontinuous at x = a

D

none of these

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A
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MCGROW HILL PUBLICATION-DIFFERENTIABILITY AND DIFFERENTIATION -EXERCISE (LEVEL 1) Single Correct Answer Type Questions
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  2. Let f(x)={{:(x^(2)-1",",,x le 1),(k(x-1)",",,x gt 1):} then

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  3. Let f be a function defined on [0,oo) by f(x)={{:(0,,x=0),((x+a//sqr...

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  4. The number of times the function y=(x^(2)+1)^(80) to be differentiated...

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  6. If 0lt alpha lt 1 and f is defind as f(x)={{:(x^(alpha),,"if "x gt 0...

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  7. Let f(x)={{:(x^(2),,"if x is rational"),(0,,"if x is irrational"):} th...

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  8. A value of k such that f(x)=x^(k) is (n-1) times differentiable at 0 b...

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  10. The derivative of sin^(-1)((1-x^(2n))/(1+x^(2n))) with respect to x^(2...

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  11. If sqrt(1-x^(6))+sqrt(1-y^(6))=a(x^(3)-y^(3)) and (dy)/(dx)=f(x,y)sqrt...

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  12. If f(x)=x^(2)+tan x and f is inverse of g, then g'(x) is equal to

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  13. Number of points of non-differentiability of f(x)=sin pi(x-[x]) in (-p...

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  14. Suppose that f is differentiable function with the property f(x+y)=f(x...

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  15. If y=f(x) satisfies f(x+y)=2f(x)+xf(y)+y(f(x))^(1//3 for all x, y in R...

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  16. If f(0)=0,f'(0)=4 and g(x)=f(-x+fof(x)) then g'(0) is equal to

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  17. If f(x)=x^(6)+e^(x//7) and fog(x)=x^(3), then g'(1) is equal to

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  18. Let (a-b cos y)(a+b cos x)=a^(2)-b^(2) and (dy)/(dx)=((sinx)f(y))/((a+...

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  19. If y=(x^(2)+1)sinx then [y(18)"("pi//2+((pi^(2))/(4)+1)] is equal to

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  20. If f(x)=cos^(2)x+cos^(2)((pi)/(3)+x)-cosx cos((pi)/(3)+x) then f(pi//8...

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