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Let f (x) = x^3-x^2-x+1 and g(x) = {max{...

Let `f (x) = x^3-x^2-x+1` and `g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2` Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).

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A DAS GUPTA-Continuity, Differentiability and Graph of Function-Exercise
  1. Let f (x) = x^3-x^2-x+1 and g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, ...

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  2. If f(x)=(e^(1/x)-1)/(1+e^(1/x)) when x!=0 =0, when x=0 show that f(x)...

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  3. Determine the values of a ,\ b ,\ c for which the function f(x)={(s...

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  4. If g(x)=(1-a^x+x a^xloga)/(x^2*a^x), x<0 ((2a)^x-xlog(2a)-1)/(x^2), x...

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

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  6. Discuss the continuity of f(x)=(lim)(nvecoo)(x^(2n)-1)/(x^(2n)+1)

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  7. The function f(x). defined as f(x)=lim(n->oo)(f(x)+x^(2n)g(x))/(1+x^(2...

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  8. Consider the function f defines by f(x) = x-[x], where[x] denotes the ...

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  9. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

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  10. Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is contin...

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  11. Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=...

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  12. Let f (x+y)=f (x) f(y) AA x, y in R , f (0)ne 0 If f (x) is continous ...

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  13. Let f : [0, 1] rarr [0, 1] be a continuous function such that f (f (x)...

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  14. The set of all points, where the function f (x) = x/(1+|x|) is dif...

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  15. The set of points where ,f(x) = x|x| is twice differentiable is

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

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

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

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

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

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

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