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Verify Mean value Theorem for the functi...

Verify Mean value Theorem for the function `f(x)= x^(2)` in the interval [2,4]

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The correct Answer is:
`c=3 in (2,4)` at f'(c )= 6
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KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-Textbook Illustrations for Practice Work
  1. If y= sin^(-1)x, show that (1 -x^(2)) (d^(2)y)/(dx^(2))-x (dy)/(dx)=0

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  2. Verify Rolle's theorem for the function y= x^(2) + 2, a = - 2 and b= 2

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  3. Verify Mean value Theorem for the function f(x)= x^(2) in the interval...

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  4. Differentiate w.r.t x, the following function: (i) sqrt(3x+2) + (1)...

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  5. Differentiate the following w.r.t x. (i) cos^(-1) (sin x) (ii) tan^...

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  6. Find f'(x) if f(x)= (sin x)^(sin x) for all 0 lt x lt pi.

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  7. For a positive constant a find (dy)/(dx), where y= a^(t + (1)/(t)), an...

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  8. Differentiate sin^(2)x w.r.t e^(cos x)

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  9. Examine the continuity of the function f(x)= 2x + 3 " at " x=1

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  10. Prove that the function f(x)= x^(2) is continuous at x=0.

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  11. Discuss the continuity of the function f given by f(x)= |x| " at " x=0...

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  12. Show that f(x)= {(x^(3)+3",",x ne0),(1",",x=0):} is a discontinuous fu...

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  13. Check the points where the constant function f(x)= k is continuous

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  14. Prove that the identity function on real numbers given by f(x)=x is co...

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  15. Is the function defined by f(x)= |x|, a continuous function

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  16. Discuss the continuity of the function f given by f(x)= x^(3) + x^(2)-...

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  17. Discuss the continuity of the function f defined by f(x)= (1)/(x), x n...

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  18. Discuss the continuity of the function f defined by f(x)= {(x+2",","if...

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  19. Find all the points of discontinuity of the function f defined by f(x)...

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  20. Discuss the continuity of the function defined by f(x) = {(x+2",","if ...

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