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Discuss the continuity and differentia...

Discuss the continuity and differentiability of `f(x)={((x-c)cos(1/(x-c)) ,, x!=c),(0 ,, x=c):}`

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. Discuss the continuity and differentiability of the function f(x)=|x...

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

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

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

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

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

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

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

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

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

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

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

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  13. 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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  14. 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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  15. If f(x)=|3-x|+(3+x), where (x) denotes the least integer greater than ...

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

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

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  18. Let f(x)={a x^2+1,x >1; x+1/2,x<=1.t h e n ,f(x) is derivable at x=1...

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  19. Show that the function defined by g(x)= "x"-"[x] is discontinuous at a...

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  20. It A is a symmetric matrix, write whether A^T is symmetric or skew - s...

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