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If f(x) is differentiable at x=a, find ...

If `f(x)` is differentiable at `x=a,` find `lim_(x->a)(x^2f(a)-a^2f(x))/(x-a).`

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The correct Answer is:
`2af(a)-a^(2)f'(a)`.
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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(b) (LONG ANSWER TYPE QUESTIONS (I))
  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. Examine the derivability of the following functions at the specified p...

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

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  5. If f(x) is differentiable at x=a, find lim(x->a)(x^2f(a)-a^2f(x))/(x...

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

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  7. Show that f(x)={{:("x sin"(1)/(x)",","when",x ne 0),(0",","when",x = 0...

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  8. Show that the function defined by f(x)=(3-2x), x lt2 and f(x)=3x-7, x ...

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  9. Discuss continuity f(x)={{:(e^(1//x)/(1+e^(1//x)),if x ne 0),(0,if x =...

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  10. Consider the following in respect of the function f(x)={{:(2+x","xge...

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

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  12. The function 'f' defined as : f(x)={{:(x^(2)+3x+a", if "xle1),(bx+c"...

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  13. For what choice of aa n db is the function f(x)={x^2,xlt=c a x+b ,x > ...

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

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  15. Show that the function f(x)=|x-3|,\ x in \ |R , is continuous but n...

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  16. Show that f(x) = |x-5| is continuous but not differentiable at x =...

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

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