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Let f(x) = {(-2sinx, x le -pi/2),(asinx ...

Let `f(x) = {(-2sinx, x le -pi/2),(asinx +b, -pi/2 lt x lt pi/2),(cosx, x ge pi/2):}` then values of a and b so that f(x) is continuous are

A

a = 1, b = 1

B

a =1, b =-1

C

a = -1, b =1

D

a = -1, b = -1

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The correct Answer is:
D
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
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  2. The points of discontinuity of f(x) = tan((pix)/(x+1))

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  3. Let f(x) = {(-2sinx, x le -pi/2),(asinx +b, -pi/2 lt x lt pi/2),(cosx,...

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

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

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

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

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

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

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

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

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

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

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

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

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

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