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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^(1//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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ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -SELF ASSESSMENT TEST (MULTIPLE CHOICE QUESTIONS)
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  4. If f (x) = 1/2 x - 1, then on the interval [0, pi]

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  5. If f(x) = 3x-5, then f^(-1) (x)

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  6. If underset( x to 0) lim [1+x log (1+b^(2))]^(1/x) = 2b sin^(2) the...

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  7. Show that the underset(xto2)lim((sqrt(1-cos{2(x-2)}))/(x-2)) doesnot e...

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  8. Let f: R to R be a positive increasing function with lim(x to infty) (...

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  9. If underset(x to infty)lim((x^(2)+x+1)/(x+1)-ax -b)=4 then

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  11. Let f : (-1,1) to R be a differentiabale function with f(0) = -1 and f...

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  12. If f: R to R is a function defined by f(x) = [x] cos((2...

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  13. Let L= lim(x to 0)(a- sqrt(a^(2)-x^(2))-x^(2)/4)/x^(4), a gt 0. If L i...

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  14. Let f: R to R be a function such that f(x+y) = f(x) + f(y) AA x, y in...

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  15. If f(x) = {{:(-x-pi/2" , " x le - pi/2),(-cos x" , " -pi/2 lt ...

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  16. Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constan...

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  17. Let f be a real valued function defined on the interval [0,infty] by f...

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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 f : (-1, 1) -> R be such that f(cos4theta) = 2/(2-sec^2theta for t...

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  20. Let f(x)={x^2 |cospi/x|, ,x !=0, x in R, x=0 then f is

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