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Let f(x)=|x| and g(x)=|x^3| , then (a).f...

Let `f(x)=|x|` and `g(x)=|x^3|` , then (a).`f(x)` and `g(x)` both are continuous at `x=0` (b) `f(x)` and `g(x)` both are differentiable at `x=0` (c) `f(x)` is differentiable but `g(x)` is not differentiable at `x=0` (d) `f(x)` and `g(x)` both are not differentiable at `x=0`

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Write the value of the derivative of f(x)=|x-1|+|x-3| at x=2 .

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  2. If f(x)=sqrt(x^2+9) , write the value of (lim)(x->4)(f(x)-f(4))/(x-4) ...

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  3. Let f(x)=|x| and g(x)=|x^3| , then (a).f(x) and g(x) both are continuo...

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  4. The function f(x)=sin^(-1)(cosx) is discontinuous at x=0 (b) continuou...

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  5. The set of points where the function f(x)=x|x| is differentiable i...

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  6. If f(x)={(|x+2|)/(tan^(-1)(x+2)),\ \ \ x!=-2 ,\ \ \ \ \ \ \ \ \ \ \ \ ...

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  7. Let f(x)=(x+|x|)|x| . Then, for all x f is continuous

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  8. The function f(x)=e^(|x|) is (a) Continuous everywhere but not differ...

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  9. The function f(x)=|cosx| is (a) everywhere continuous and differe...

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

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

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

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

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

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

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

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

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

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

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