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Let f(x) = [x] and g(x) = {{:(0",",x in ...

Let `f(x) = [x] and g(x) = {{:(0",",x in Z),(x^(2)",",x in R - Z):}`, then (where `[*]` denotes greatest integer function)

A

`underset(x to 1)` exists, but g(x) is not continuous at x=1

B

`underset(x to 1)lim `does not exist and f(x) is not continuous at `x=1`

C

gof is continuous for all x

D

fog is continuous for all x

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OBJECTIVE RD SHARMA ENGLISH-CONTINUITY AND DIFFERENTIABILITY-Exercise
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  2. If f(x)=xsin1/x ,\ x!=0 , then the value of the function at x=0 , s...

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

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

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

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

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

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

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

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  10. Let f(x)={{:(,x^(n)sin\ (1)/(x),x ne 0),(,0,x=0):} Then f(x) is contin...

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  11. If 4x+3|y|=5y, then y as a function of x is

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  12. If f(x)=x^3sgn(x), then

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  13. For a real number y, Let [y] denotes the geatest integer less than ...

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  14. If f(x)={{:(,x^(2)sin((1)/(x)),x ne 0),(,0, x=0):}, then

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  15. The following functions are differentiable on (-1,2)

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  16. If f(x)=sqrt(x+2sqrt(2x-4))+sqrt(x-2sqrt(2x-4)) then the value of 10 f...

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  17. The derivative of f(x)=|x|^(3) at x=0, is

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  18. If f (x) = x (sqrtx+sqrt((x+1)), then

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  19. Write the value of the derivative of f(x)=|x-1|+|x-3|"\ "a t"\ "x=3.

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  20. If f(x)=[x sin pix], then which of the following, is incorrect,

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