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If the function f(x) = {{:((x^(2)-(a+2)x...

If the function `f(x) = {{:((x^(2)-(a+2)x + a)/(x-2),,x ne 2),(2,,x = 2):}` is continuous at x = 2, then :

A

1

B

0

C

(-1)

D

3

Text Solution

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The correct Answer is:
B
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HIMALAYA PUBLICATION-LIMITS, CONTINUITY AND DIFFERENTIABILITY-QUESTION BANK
  1. If f(x) = {((x^(5)-32)/(x-2), x ne 2),(k, x =2):} is continuous at x =...

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  2. The points of discontinuity of f(x) = tan((pix)/(x+1))

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  3. If the function f(x) = {{:((x^(2)-(a+2)x + a)/(x-2),,x ne 2),(2,,x = 2...

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  4. The value of f(0) so that the function f(x) = (2x-sin^(-1)x)/(2x+tan^(...

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  5. How should we define f(x) = (log(1+ax)-log(1-bx))/x at x = 0 so as to...

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  6. Which of the following is false ?

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  7. If f(x)={{:(xsin((1)/(x))", if "xne0),(0" , if "x=0):} then at x=0 th...

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  8. Let f(x) = {((sin pix)/(5x), x ne 0),(k, x =0):} If f(x) is continuous...

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  9. The function f(x)=|x|+(|x|)/(x) is

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  10. If f(x)={((1-cosx)/(x),xne0),(k, x=0):} is continuous at x=0 then k=

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  11. If f(x) = {((sin 5x)/(x^(2)+2x), x ne 0),(k+1/2, x =0):} is continuous...

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  12. Which one of the following is not true always?

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  13. The points of discontinuity of f(x) = tan((pix)/(x+1))

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

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

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

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

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

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