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Verify Mean Value Theorem, if f(x) = x^3...

Verify Mean Value Theorem, if `f(x) = x^3-5x^2-3x`, in the interval [a, b], where a = 1 and b = 3. Find all `c in (1,3)` for which `f'(c) = 0`.

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

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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 : cos^-1(x/2)/sqrt(2x+7), x lies b...

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  9. Differentiate w.r.t. x the function : cot^-1[(sqrt(1+sinx) + sqrt(1-si...

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

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

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  12. Differentiate w.r.t. x the function : (sinx - cosx)^(sinx-cosx), x lie...

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

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

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

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

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

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  18. If (x-a)^2 + (y-b)^2 = c^2 , for some c > 0, prove that [1+(dy/dx)^2]...

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

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

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