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The value of p and q for which the funct...

The value of p and q for which the function
`f(x) = {((sin(p+1)x+sinx)/(x), ",",x lt 0),(q, ",", x = 0),((sqrt(x+x^(2))-sqrt(x))/(x^(3//2)), ",", x gt 0 ):}`
is continuous for all x in R, are

A

`p = 1/2, q = -3/2`

B

`p = 5/2, q = 1/2`

C

`p = -3/2, q = 1/2`

D

`p = 1/2, q = 3/2`

Text Solution

Verified by Experts

The correct Answer is:
C
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TARGET PUBLICATION-CONTINUITY-Competitive Thinking
  1. If f(x) = {((|x-a|)/(x-a), ",","when"x != a),(1, ",", "when"x = a ):} ...

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  2. The function f(x) = |x| = (|x|)/x is

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  3. The points of discontinuity of the function f(x)=(2x^(2)+7)/(x^(3)+3x...

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  4. If f: R to R is defined by f(x) = {(x-1, ",","for"x le 1),(2-x^(2),...

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  5. The number of points at which the function f(x) = 1/(log|x|) is discon...

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  6. The number of discontinuities of the greatest interger function f(x) =...

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  7. If the function f(x) = {(5x-4, ",","if"0 lt x le 1),(4x^(2)+3bx, ","...

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  8. Let f(x) = {((x^(3)+x^(2)-16x+20)/((x-2)^(2)), ",","if" x != 2),(k, ",...

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  9. The function f(x) = Sin(x)/[[x]] , where [x] the greatest function at ...

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  10. The function f(x) = sin{x} is where {.} is fractional part function

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  11. Let f(x) = (1-tanx)/(4x-pi), x != (pi)/4, x in [0,(pi)/2]. If f(x) is ...

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  12. If the function f9x)=(2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at ea...

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  13. The function f(x) = {(x+2, ",",1 le x lt 2),(4, ",", x = 2 ),(3x-2, "...

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  14. The value(s) of x for which the function f(x) = {(1-x, ",", x lt 1),...

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  15. If f(x) is continuous over [-pi, pi], where f(x) is defined as f(x) ...

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  16. Let f(x) = {(-2sin x, ",","if" x le -(pi)/2),(A sin x + B, ",", "if"-(...

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  17. The value of p and q for which the function f(x) = {((sin(p+1)x+sinx...

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  18. Q. For every integer n, let an and bn be real numbers. Let function f:...

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  19. Let a function f: R to R, where R is the set of real nos. satisfying t...

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  20. The value of f(0) so that the function f(x) = (sqrt(1+x)-(1+x)^(1/3)...

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