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The value of f(0) so that f(x)=((4^(x)-1...

The value of f(0) so that `f(x)=((4^(x)-1)^(3))/(sin(x//4)log(1+x^(2)//3))` is continuous everywhere is

A

`3(log 4)^(3)`

B

`4 (log 4)^(3)`

C

`12(log 4)^(3)`

D

`15(log 4)^(3)`

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)=(log(1+x//a)-log(1-x//b))/(x) is contin...

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

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  4. If f(x)=((a^(x)-1)^(3))/(sin (x log a)log (1+x^(2) log a^(2)) is conti...

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  5. If If {{:(,(72^(x)-9^(x)-8^(x)+1)/(sqrt2-sqrt(1+cosx)),x ne 0),(,k log...

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  6. If f : R to R is continuous such that f(x + y) = f(x) + f(y) x i...

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  7. Let f be a non zero continuous function satisfying f(x+y)=f(x) f(y) fo...

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  8. Given that the function f defined by f(x)={{:(,2x-1,"if "x gt 2),(,k,"...

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  9. f(x) = (x^(3) + x^(2) - 16 x + 20)/((x - 2)^(2)) " if " x ne 2 , = k ...

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

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  11. Let f(x) = (x + x^(2) + ...+ x^(n)-n)/(x -1), x ne 1, the value of f (...

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  12. If the function f(x)=(sin 3x)/(x)" for "x ne 0 and f(0)=k/2 is continu...

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  13. If f(x)={{:((sqrt(1+kx)-sqrt1-kx)/(x),"for" -1 le x0),(2x^(2)+3x-2,"fo...

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  14. If : [ -2 ,2 ] to R is defined by f(x) = {: { ((sqrt(1+cx) -sqr...

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  15. Let f(x)=-2 sin x, if x le (-pi)/(2), f(x)=a sin x+b," if "(-pi)/(2), ...

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  16. If [x] denotes the greatest integer not exceeding x and if the functi...

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

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  18. Let f: R to R is defined by f(x)= {{:(,alpha+(sin [x])/(x),if x gt 0),...

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  19. If R rarr R b e defined f(x)={{:(a^(2)cos^(2) x+b^(2) sin^(2)x,if xle0...

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  20. f : R - {0} to R " given by " f(x) = (1)/(x) - (2)/(e^(2x)-1) can b...

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