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If f(x)={{:(,(x log cos x)/(log(1+x^(2))...

If f(x)=`{{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):}` then

A

f is continuous at x = 0

B

f is continuous at x = 0 but not differentiable at x = 0

C

f is differentiable at x = 0

D

f is not continuous at x = 0

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The correct Answer is:
A, C
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ARIHANT MATHS-CONTINUITY AND DIFFERENTIABILITY-Exercise (More Than One Correct Option Type Questions)
  1. If f(x) = |x+1|(|x|+|x-1|), then at what points the function is/are no...

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  2. Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) ...

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  3. If f(x) = {{:((sin^(-1)x)^(2)cos((1)/(x))",",x ne 0),(0",",x = 0):} th...

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  4. Q. Let f(x)=cos x $ H(x)=[min [f(t) 0<=t<=x for 0<=x<=p...

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  5. If f(x) = 3(2x + 3)^(2//3) + 2x + 3, then

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

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  7. If f(x)={{:(,(x log cos x)/(log(1+x^(2))),x ne 0),(,0,x=0):} then

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  8. Let [x] denotes the greatest integer less than or equal to x. If f(x) ...

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  9. The function, f(x)=[|x|]-|[x]| where [] denotes greatest integer funct...

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  10. The function f(x)=sqrt(1-sqrt(1-x^2))

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  11. Consider the function f(x) = |x^(3) + 1|. Then,

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  12. f is a continous function in [a, b]; g is a continuous function in [b,...

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  13. Which of the following function(s) has/have the same range ?

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  14. If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points ...

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  15. Let f(x)={{:(,x^(n)"sin "(1)/(x),x ne 0),(,0,x=0):} Then f(x) is conti...

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  16. A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0)...

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  17. Let f(x) = int(-2)^(x)|t + 1|dt, then

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  18. A function f(x) satisfies the relation f(x+y) = f(x) + f(y) + xy(x+y),...

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  19. If f(x) = {{:( 3x ^(2) + 12 x - 1",", - 1 le x le 2), (37- x",", 2 lt...

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  20. If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0, then for x...

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