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Show that f(x)={{:(|2x-3|[x]", "xge1),(s...

Show that `f(x)={{:(|2x-3|[x]", "xge1),(sin((pix)/2)", "xlt1):}` is continuous but not differentiable at x = 1.

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MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-REVISION EXERCISE
  1. Show that f(x)={{:(|2x-3|[x]", "xge1),(sin((pix)/2)", "xlt1):} is ...

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  2. Does there exist a function which is continuous everywhere but not ...

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

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  4. Find, from first principle, the derivative of sin^(-1)x/x w.r.t. x.

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  5. Differentiable the following w.r.t. x : sqrt(3x+2)+1/(sqrt(2x^(2)+4)...

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  6. Differentiable the following w.r.t. x : e^(sec^(2)x)+3cos^(-1)x.

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  7. Differentiate the following w.r.t. x : f(x)=log[(2-x)^(1//2)(x^(2)-1...

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  8. Differentiate the following function w.r.t x : tan^(-1) ((sqrt(1+x) - ...

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  9. Differentiate the following w.r.t. x: (3x^(2)-9x+5)^(9)

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  10. Differentiate the following w.r.t. x: sin^(3)x+cos^(6)x

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  11. Differentiate the following w.r.t. x: e^(log(x+sqrt(x^(2)+a^(2))))

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  12. Differentiate the following w.r.t. x: e^(2logx+3x)

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  13. Prove that (cot^(-1)x+"cot"^(-1)1/x) is a constant.

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  14. If y=f((2x-1)/(x^2+1)) and f^(prime)(x)=sinx^2 , find (dy)/(dx) .

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  15. Find the derivative of the following w.e.t. x : 3/(root(3)(x))-5/cos...

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  16. Find the derivative of the following w.e.t. x : log(1/sqrtx)+5x^(a)-...

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  17. If y=tan^(-1)((e^(2x)+1)/(e^(2x)-1)), prove that : dy/dx=-(2e^(2x))/...

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  18. If the derivative of tan^(-1)(a+b x) takes the value 1 at x=0, prove t...

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  19. Using the fact that s in (A + B) = s in A cos B + cos A s in Band the ...

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  20. If sqrt(y+x) +sqrt(y-x) =c show that dy/dx = y/x -sqrt((y^2/x^2)-1)

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