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The value of f(0) so that the function f...

The value of f(0) so that the function `f(x)=((27-2x)^(1//3)-3)/(9-3(243+5x)^(1//5))" is continuous at x=0 is "`

A

`2//3`

B

6

C

2

D

none

Text Solution

Verified by Experts

The correct Answer is:
C
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DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. The value of f(0) so that f(x)=(sqrt(1+x)-1)/(x) is continuous at x=0 ...

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  2. If f(x)=x^(1/(x-1))" for "x ne 1 and if f is continuous at x=1 then f(...

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  3. The value of f(0) so that the function f(x)=((27-2x)^(1//3)-3)/(9-3(24...

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  4. In order that the function f(x)=(x+1)^(cot x) is continous at x=0, f(0...

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  5. The value of f(00) so that the function f(x)=(2x-Sin^(-1)x)/(2x+Tan^(-...

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  6. The value of f(0) so that the function f(x)=(sqrt(1+x)-root3(1+x))/(x)...

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  7. The value of f(0) so that f(x)=(cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+1)-1 ...

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  8. Extend the definition of the following by continuity f(x)=(1−cos7(x−π)...

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  9. Let f(x)=(1-tan x)/(4x-pi), x ne pi/4, x in [0,pi/2]." If f(x) is cont...

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  10. f(x) ={{:((1-sqrt(2)sin x)/(pi -4x),"if "x ne (pi)/(4)),("k","if "x=(p...

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  11. If f: R to R is defined by f(x)={{:(,(1+3x^(2)-cos2x)/x^(2),"for "x ne...

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  12. If f: R to R" is defined by f(x)"={{:(,(cos 3x-cosx)/(x^(2)),"for "x n...

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  13. If f R to R is defined by <by> f (x) = {{:(( 2 sin x - sin 2x)/(2x ...

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  14. The value of f(0) so that the function f(x)=(1-cos (1-cos x))/(x^(4)) ...

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  15. Find the value of AO) so that the function f(x) = ((a+x)^(2)sin(a+x)-a...

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  16. The value of f(2) so that f(x)=(2^(x+2)-16)/(4^(x)-16) is continuous a...

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  17. If the function f(x)=(log(1+ax)-log(1-bx))/(x) is continuous at x=0, t...

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  18. The value of f(0) so that f(x)=(log(1+x//a)-log(1-x//b))/(x) is contin...

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  19. Let f(x)=(log(1+x+x^(2))+log(1-x+x^(2))/(sec x-cos x),x ne 0. Then the...

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  20. The value of f(0) so that f(x)=((4^(x)-1)^(3))/(sin(x//4)log(1+x^(2)//...

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