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Show that the function f(x)={x^m sin(1/x...

Show that the function `f(x)={x^m sin(1/x) , 0 ,x != 0,x=0` is differentiable at `x=0`,if `m > 1` and continuous but not differentiable at `x=0`,if `0ltmlt1`.

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Show that f(x)=(x)^(1/3) is not differentiable at x=0.

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  2. Show that f(x)=|x-3| is continuous but not differentiable at x=3.

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  3. Show that the function f(x)={x^m sin(1/x) , 0 ,x != 0,x=0 is different...

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  4. Discuss the continuity and differentiability of the function f(x)=|x...

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  5. Show that the function f defined as follows f(x)={(3x-2 ,, 0ltxle1...

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  6. Discuss the continuity and differentiability of f(x)={((x-c)cos(1/(x...

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  7. Write an example of a function which is everywhere continuous but f...

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  8. Discuss the continuity and differentiability of f(x)=|log|x||

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  9. If f is defined by f(x)=x^2-4x+7, show that f^(prime)(5)=2f^(prime)...

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  10. If f is defined by f(x)=x^2, find f^(prime)(2)dot

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  11. Find the derivative of the function f defined by f(x)=m x+c at x=0.

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  12. Discuss the continuity and differentiability of f(x)=e^(|x|)dot

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  13. If for the function varphi(x) = lambdax^2+7x-4 , varphi' (5) = 97, ...

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  14. Is |sinx| differentiable ?What about cos|x|?

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  15. The set of points where the function f(x) given by f(x)=|x-3|cosx is d...

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  16. 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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  17. If f(x)={1/(1+e^((1,)/x)),x!=0 0,x=0,t h e nf(x) is continuous as well...

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  18. If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than ...

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  19. Let f(x)=a+b|x|+c|x|^4 , where a , ba n dc are real constants. Then, f...

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

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