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Show that the function f(x) = {{:(-x^2, ...

Show that the function `f(x) = {{:(-x^2, x le 0),(x^2 ,x gt 0):}` is continuous at `x = 0`. Also show that f is differentiable at `x = 0`.

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Examine for continuity the following functions: f(x) = {:(x^2, if x ...

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  2. Let f(x) = x+ |x|. Show that f is continuous but not derivable at x = ...

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  3. Show that the function f(x) = {{:(-x^2, x le 0),(x^2 ,x gt 0):} is con...

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

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  5. Find ainR so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0...

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  6. Examine the differentiability of the function 'f' defined by: f(x) =...

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

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  8. If f(x) = e^x, find f' (3) starting from defination

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  9. If f(x) = e^(sqrtx) find f' (x) .

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  10. A function f : R rarr R satisfies the equation f(x + y) = f(x).f(y) fo...

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  11. If f(x) = log (2x-1), find f'( c ) .

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  12. If f(x) = {{:(x((e^(1//x) - e^(-1//x))/(e^(1//x)+e^(-1//x)))",",x ne 0...

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  13. Find f'(X) using first prinicples when f(x) =e^(3x -2)

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  14. Find f'(X) using first prinicples when f(x) = log(2x +3)

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  15. Find derivative of each of the following functions: e^x + log x

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  16. Find derivative of each of the following functions: x^2 logx

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  17. Find derivative of each of the following functions: (logx)/x

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  18. Find derivative of each of the following functions: e^x/(1+x^2)

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  19. Find derivative of each of the following functions: (e^x sin x)/(sec...

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  20. Find derivative of each of the following functions: (e^x log x)/(x^2...

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