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If 'f' is differentiable at x = a, find ...

If 'f' is differentiable at x = a, find `(underset(xrarra)lim(x^2f(a)-a^2f(x))/(x-a))`

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Examine the derivability of the following functions at the specified p...

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  2. Examine the derivability of the following functions at the specified p...

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  3. If 'f' is differentiable at x = a, find (underset(xrarra)lim(x^2f(a)-a...

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  4. If F(x) = f(Ax) and f(ax) is differentiable , then prove that F'(x) = ...

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  5. If f(x) = {:{(xsin(1/x),xne0),(0,x=0):} Show that 'f' is not different...

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  6. Show that the function defined by: f(x) : {:{(3-2x,ifx<2),(3x-7,ifxg...

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  7. Discuss the continuity of fx) at x =0, when: f(x) = {:{((e^(1//x) -1...

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  8. Show that the function: f(x) = {:{(2+x,ifxge0),(2-x,ifx<0):} is cont...

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  9. Show that the function 'f' defined as follows, is continuous at x = 2,...

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  10. The function 'f' defined as: f(x) = {:{(x^2+3x+a,ifxle1),(bx+2,ifx>1...

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  11. For what values of 'a' and 'b' the function: f(x) = {:{(x^2,xlec),(a...

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  12. Let f: R rarr R(R is the set of real numbers) be defined as follows: ...

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  13. Show that f(x) = |x-3|, x in R is continuous but not differentiable at...

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  14. Write an example of a function, which is continuous everywhere but fai...

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  15. Use Chain Rule to find the derivatives of the following: f(x) = (1-2...

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  16. Find the derivatives of the following: f(x) =(x^2+3x+4).

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  17. Use Chain Rule to find the derivatives of the following: f(x) = (3x^...

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  18. Use Chain Rule to find the derivatives of the following: f(x)=(2x^2+...

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  19. Use Chain Rule to find the derivatives of the following: f(x)=3/(2-x...

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  20. Find the derivatives of the following: h(x) = (x+1)(x+2)(x+3)

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