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If f(x)= {((x^(2))/(a)-a",",x lt a),(0",...

If `f(x)= {((x^(2))/(a)-a",",x lt a),(0",",x=a),(a-(x^(2))/(a)",",x gt a):}` then, ………

A

`underset(x rarr a^(+))("lim") f(x)= a`

B

`underset(x rarr a)("lim") f(x)= -a`

C

f is continuous at x=a

D

f is differentiable at x=a

Text Solution

Verified by Experts

The correct Answer is:
C
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook based MCQs
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  2. If f(x)= {(ax+b,1le x lt 5),(7x-5,5 le x lt 10),(bx + 3a,x ge 10):} is...

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  3. If f(x)= {((x^(2))/(a)-a",",x lt a),(0",",x=a),(a-(x^(2))/(a)",",x gt ...

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  4. If f(x)= {(x",",x in {0, 1}),(1",",x ge 1):} then, ……

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  5. (d)/(dx). ((1)/(log|x|))= …….

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  6. If y= a sin x + b cos x then, y^(2) + (y(1))^(2)= ……. (a^(2) + b^(2) n...

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  7. (d)/(dx) (x^(2) + sin^(2) x)^(3) =…….

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  8. (d)/(dx) ( sqrt(x sin x))= …… (0 lt x lt pi)

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  9. (d)/(dx) (e^(sin^(-1)x + cos^(-1) x))= …….(|x| lt 1)

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  10. If function f(x) is continuous at x= 0, f(x)= {((sin (4x))/(9x)",",x n...

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  11. If x= a t^(2), y= 2 a t" then " (dy)/(dx) = …., where t ne 0

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  12. (d)/(dx) (log(5) x^(2))= ……..

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  13. Derivative of tan^(-1)x w.r. to cot^(-1)x is ……. Where x in R

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  14. If y= log (x + sqrt(x^(2) + a^(2))) then (dy)/(dx)= ………

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  15. If y= log(10) sin x then (dy)/(dx) = ……..

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  16. y= sqrt(sin x + sqrt(sin x + sqrt(sin x + …….oo))) then (dy)/(dx)=………

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  17. f(x)= x^(2) e^(2(x-1)), 0 lt x lt 1 and f(x) = a "sgn" (x+1) cos (2x-2...

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  18. The value of f(0), so that f(x)= (sqrt(a^(2)-ax + x^(2))-sqrt(a^(2) + ...

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  19. f(x+ y) = f(x) f(y), For AA x and y. If f(3)= 3 and f'(0) =11 then f'(...

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