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If the function f(x) = {((sin 3x)/x, x n...

If the function `f(x) = {((sin 3x)/x, x ne 0),(k/2, x = 0):}` is continuous at x = 0, then k =

A

3

B

6

C

9

D

12

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A
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. Let f(x) = (1-tanx)/(4x-pi),x ne (pi)/(4), x in [0, (pi)/(2)], if f(x)...

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  2. Consider f(x)={{:((x^(2))/(|x|)","x!=0),(0","x=0.):}

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  3. If the function f(x) = {((sin 3x)/x, x ne 0),(k/2, x = 0):} is continu...

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  4. If f(x) = (x^(2)-10x +25)/(x^(2)-7x+10 for x ne 5 and f is continuous ...

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  5. If f : R rarr R is defined by f(x) ={(a^(2)cos^(2)+b^(2)sin^(2)x, x le...

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  6. If f(x) ={((sqrt(1+kx)- sqrt(1-kx))/x, -1 le x le0),(2x^(2)+3x-2, 0 le...

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  7. If f(x) = {((1-sqrt2sinx)/(pi-4x), x ne pi/4),(a, x = pi/4):} is conti...

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  8. The value of b for which the function : f(x) = {{:(5x-4,"if",0lt x le ...

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  9. The value of f(x) at x = 0, so that the function f(x) = (2^(x)-2^(-x))...

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  10. The function f(x) = (log (1+ax) - log(1-bx))/(x) is not defined at x =...

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  11. The function f(x) = [x], where [x] denotes the greatest integer not gr...

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  12. If f(x)={{:((logex)/(x-1),,,x ne 1),(k,,,x=1):}is continuous at x = 1...

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  13. f(x)=2a-x in -altxlta=3x-2a in a lex. Then which of the following i...

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  14. Which of the following function is differentiable at x=0?

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  15. Let f(x) = (1-tanx)/(4x-pi),x ne (pi)/(4), x in [0, (pi)/(2)], if f(x)...

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  16. The function f : R//{0} rarr R given by : f(x) = (1)/(x) - (2)/(e^(2...

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  17. If f : R rarr R is defined by f(x) = {((cos3x-cosx)/x^(2), x ne 0),(la...

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  18. f(x) = (sqrt(1+px) - sqrt(1 - px))/(x), -1 le x le 0 = (2x + 1)/(x-2),...

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  19. Let f(x) = {(x^(4)-5x^(2)+4)/(|(x-1)(x-2)|) x ne 1,2),(6, x=1), (12, x...

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  20. Let f(x) = (1-sin x)/((pi - 2x)^(2)),"where x" ne pi//2 and f(pi//2) =...

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