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If `f: R to R` is defined by `f(x)={{:(,(1+3x^(2)-cos2x)/x^(2),"for "x ne 0),(,k,"for x=0"):}`

A

1

B

5

C

6

D

0

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DIPTI PUBLICATION ( AP EAMET)-LIMITS AND CONTINUITY-Exercise 1C(Continuity)
  1. 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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  2. f(x) ={{:((1-sqrt(2)sin x)/(pi -4x),"if "x ne (pi)/(4)),("k","if "x=(p...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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