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Examine the applicability of Mean Value ...

Examine the applicability of Mean Value Theorem for all three functions given in the above exercise 2. (i) f(x) = [x] for x ∈ [5,9] (ii) f(x) = [x] for x ∈ [-2,2] (iii) f(x) = [xsqrt -1] for x ∈ [1,2]

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PRADEEP PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE
  1. Verify Mean Value Theorem, if f(x) = x^2-4x-3, in the interval [a, b],...

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  2. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

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  3. Examine the applicability of Mean Value Theorem for all three function...

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

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  5. Differentiate w.r.t. x the function : sin^3x + cos^6 x

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  6. Differentiate w.r.t. x the function : (5x)^(3cos2x)

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  7. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

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  8. Differentiate w.r.t. x the function : (logx)^logx, x>1

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  9. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

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  10. Differentiate w.r.t. x the function : x^x + x^a + a^x + a^a, for some ...

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  11. Differentiate w.r.t. x the function : x^(x^2-3) + (x-3)^(x^2), for x>...

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  12. Find dy/dx if y =12(1-cost), x =10(t-sint)

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  13. Find dy/dx if y = sin^-1x + sin^-1 sqrt(1-x^2), 0ltxlt1

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  14. If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that ...

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  15. If cosy = xcos(a+y), with cos a ne +-1, prove that dy/dx = (cos^2(a+y...

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  16. If x = a(cost + t sint) and y = a(sint - tcost), find (d^2y)/dx^2

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  17. If f(x) = |x|^3 show that f''(x) exists for all real x and find it.

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  18. Using mathematical induction prove that d(x^n)/dx = nx^(n-1) for all p...

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  19. Using the fact that sin(A+B) = sinA cosB + cosA sinB and the differen...

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

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