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If the function f(x)={(cosx)^(1/x),x!=0k...

If the function `f(x)={(cosx)^(1/x),x!=0k ,x=0` is continuous at `x=0` , then the value of `k` is (a)`0` (b) `1` (c) `-1` (d) None of these

A

0

B

1

C

`-1`

D

e

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. The function f(x)={(e^(1/x)-1)/(e^(1/x)+1),x!=0 0,x=0 is continuous a...

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  2. Let f(x) ={{:((x-4)/(|x-4|)+a,xlt4),(a+b,x=4),( (x-4)/(|x-4|)+b, x gt4...

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  3. If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , t...

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  4. If the function f(x)=|x|+|x-1|, then

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  5. Let f(x)={(x^4-5x^2+4)/(|(x-1)(x-2)|)\ \ \ \ ,\ \ \ x!=1,\ 1 6\ \ \ \ ...

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  6. If the function f as defined below is continuous at x=0find the values...

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  7. If f(x)=[{:(mx+1,if x le (pi)/(2)),(sinx+n,ifxgt(pi)/(2)):} is contin...

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  8. The value of f(0), so that f(x)=(sqrt(a^(2)-ax+x^(2))-sqrt(a^(2)+ax+x^...

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  9. (a) Draw the graph of f(x) = ={{:(1",",, |x| ge 1), ((1)/(n^(2)) ",",,...

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  10. The value of f(0), so that the function f(x)=((27-2x)^2-3)/(9-3(243+5x...

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  11. The value of f(0) so that the function f(x)=(2-(256-7x)^(1/8))/((5x+32...

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  12. The following functions are continuous on (0, pi) (a) tan x (b)under...

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  13. If f(x)=xsin1/x ,\ x!=0 , then the value of the function at x=0 , s...

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  14. Let f(x) = [x] and g(x) = {{:(0",",x in Z),(x^(2)",",x in R - Z):}, th...

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  15. Let f(x) = lim( n to oo) m ( sin x)^(2n) then which of the follow...

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  16. Let f(x) be a function differentiable at x=c. Then underset(x to c)lim...

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  17. If (lim)(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of...

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  18. if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):}

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  19. The function f(x)=|x|+|x-1| is

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  20. For the function f(x)={{:(,|x-3|,x ge 1),(,(x^(2))/(4)-(3x)/(2)+(13)/(...

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