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Let f(x) = {{:(x^(2)/2", ...

Let ` f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3/2", "1lexle2):}`
Discuss the continuity of f, f' and f'' on [0, 2].

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A DAS GUPTA-Continuity, Differentiability and Graph of Function-Exercise
  1. The set of points where ,f(x) = x|x| is twice differentiable is

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  2. Let f(x) be difined in the interval [-2, 2] such that f(x)={{:(-1"...

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  3. Let f(x) = {{:(x^(2)/2", "0 lexlt1),(2x^(2)-3x+3...

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  4. Draw the graph of the function and discuss the continuity and differen...

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  5. Given the function f(x) = 1/( 1-x) , The points of discontinuity of th...

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  6. If f(x)={:{(ax^(2)-b", for " 0 le x lt1),(2", for " x=1),(x+1", for " ...

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  7. If f(x)={(((1-sin^(3)x))/(3cos^(2)x)",",x lt (pi)/(2)),(a",",x=(pi)/(2...

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  8. Let f(x)=( x^2+3x-10)/(x-2), x=!2. The value f(2) = will make the fun...

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  9. If f(x) is continuous in [0,1] and f(1/2)=1. prove that lim(n->oo)f((...

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  10. If f(x) =(sin (e^(x-2)-))/(log(x-1)) then lim(xto2)f(x) is given by

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  11. If f(x)={((sqrt(1+px)-sqrt(1-px))/(x) ",", -1 le x lt 0),((2x+1)/(x-2...

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  12. The function f(x) = (log(1+ax)-log(1-bx))/x is not difined at x = 0. ...

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  13. The function f(x)={{:(|x-3|",", x ge1),(((x^(2))/(4))-((3x)/(2))+(13)/...

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  14. The range of the function f(x)=(tan(pi[x+1]))/(x^(4)+1) (where, [.] is...

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  15. The function f(x)=1+|sin x|, is

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  16. If x+ |y|=2 y, then y as a function of x is

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  17. The graph of the function, cos x cos (x +2) -cos^2 (x+1) is

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  18. यदि f(x)=x[sqrt(x)-sqrt((x+1))] हो तो-

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  19. Let f(x)=lim(ntooo)(1-x^n)/(1+x^n). Then

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  20. If both f(x) and g(x) are non-differentiable at x=a then f(x)+g(x) may...

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