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If f(2)=4 and f^(prime)(2)=1 , then find...

If `f(2)=4` and `f^(prime)(2)=1` , then find `(lim)_(x->2)(x\ f(2)-2f\ (x))/(x-2)` .

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RD SHARMA ENGLISH-DIFFERENTIABILITY-All Questions
  1. If f(x) is differentiable at x=a , find (lim)(x->a)(x^2f(a)-a^2\ f(x))...

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  2. For what choice of a and b is the function f(x)={x^2\ \ \ ,\ \ \ xlt=c...

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  3. If f(2)=4 and f^(prime)(2)=1 , then find (lim)(x->2)(x\ f(2)-2f\ (x))/...

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  6. Show that f(x)=x^(1//3) is not differentiable at x=0 .

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  7. Show that f(x)={12 x-13 ,\ \ \ if\ xlt=3 \ \ \ \ \ 2x^2+5,\ \ \ \ \ i...

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  10. Find whether the following function is differentiable at x = 1 and x...

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  13. Show that the function f(x)={x^msin(1/x),\ \ \ x!=0 0,\ \ \ \ \ \ \ \...

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  16. If f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ ...

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  18. If f(x)=x^2+2x+7 , find f\ '\ (3) .

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  19. Find f\ '\ (2) and f\ '\ (5) when f(x)=x^2+7x+4 .

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  20. For the function f given by f(x)=x^2-6x+8 , prove that f\ '\ (5)=4 .

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