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The function f(x)=(sin(pi[x-pi]))/(4+[x]...

The function `f(x)=(sin(pi[x-pi]))/(4+[x]^2)` , where `[]` denotes the greatest integer function,(a) is continuous as well as differentiable for all `x in R` (b) continuous for all `x` but not differentiable at some `x` (c) differentiable for all `x` but not continuous at some `x` . (d) none of these

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. The function f(x)=|cosx| is (a) everywhere continuous and differe...

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  2. If f(x)=sqrt(1-sqrt(1-x^2)) , then f(x) is (a) continuous on [-1, 1] ...

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  3. If f(x)=a|sinx|+b\ e^(|x|)+c\ |x|^3 and if f(x) is differentiable at x...

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  4. If f(x)=x^2+(x^2)/(1+x^2)+(x^2)/((1+x^2)^2)+. . . . +(x^2)/((1+x^2)^n)...

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  5. If f(x)=|(log)e x| , then (a) f'(1^+)=1 (b) f^'(1^(-))=-1 (c) f'...

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  6. If f(x)=|(log)e|x|| , then (a)f(x) is continuous and differentiable ...

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  7. Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is c...

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  8. The function f(x)=x-[x] , where [⋅] denotes the greatest integer fu...

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  9. Let f(x)={a x^2+1,\ \ \ \ \ x &gt;1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 ...

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  10. Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. ...

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  11. Let f(x)=|cosx| (a) Then, f(x) is everywhere differentiable (b) f(x)...

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  12. The function f(x)=1+|cosx| is (a) continuous no where (b) continuou...

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  13. The f(x)=|cosx| (a)Then, f ( x ) is everywhere differentiable at x=(...

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  14. The function f(x)=(sin(pi[x-pi]))/(4+[x]^2) , where [] denotes the gre...

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  15. Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. Th...

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  16. If f(x)=|3-x|+[3+x] , where [x] denotes the least integer greater th...

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  17. If f(x)={1/(1+e^(1//x)),\ \ \ \ x!=0 0,\ \ \ \ \ \ \ \ \ \ \ x=0 , the...

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  18. If f(x)={(1-cosx)/(xsinx),x!=0 and 1/2,x=0 then at x=0,f(x) is (a)c...

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  19. The set of points where the function f(x) given by f(x)=|x-3|cosx i...

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  20. Let f(x)={1, x <= -1, |x|, -1 < x < 1, 0, x >=1 . Then, f is (a) c...

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