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Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(...

Let `f(x) = (sin (pi [ x + pi]))/(1+[x]^(2))` where [] denotes the greatest integer function then f(x) is

A

continuous and differentiable at all ` x in R `

B

continuous but not differentiable at some x

C

Differentiable but not continuous at x =0

D

Neither continuous nor differentiable at x =0

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The correct Answer is:
A
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AAKASH INSTITUTE-CONTINUITY AND DIFFERENTIABILITY-Assignment ( section -A)
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  3. If y="log"(2)"log"(2)(x), then (dy)/(dx) is equal to

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  4. if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

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  8. The value of c in Lagrange's mean value theorem for the function f(x) ...

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  11. If f(x)=sqrt(1-sqrt(1-x^2) then at x=0

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  12. Domain of differentiable of the function f(x) = |x -2| cos x is

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  13. Let f(x) = (sin (pi [ x + pi]))/(1+[x]^(2)) where [] denotes the great...

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  14. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+ ....oo term then at x=0,f...

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  15. Let f(x)={(|x+1|)/(tan^(- 1)(x+1)), x!=-1 ,1, x!=-1 Then f(x) is

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  17. If y = (e^(x)+1)/(e^(x)-1), " then" (y^(2))/2 + (dy)/(dx) is equal to

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  18. If f(x)=e^(x)g(x),g(0)=2,g'(0)=1, then f'(0) is

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  19. If ax^(2)+2hxy+by^(2)=0,"show that "(d^(2)y)/(dx^(2))=0

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  20. Derivative of the function f(x) = log(5) (log(8)x), where x > 7 is

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