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The number of distinct real roots of x^4 – 4x^3 + 12x^2 + x – 1 = 0 is...
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Mar 29, 2019
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Verify Rolle’* theorem for the function f(x) = log {(x^2 + ab)/(x(a + b))} on [a, b], where 0 < a < b.
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Mar 28, 2019
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Prove that sin(x+y)/sin(x-y) = (tanx+tany)/(tanx-tany)
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Mar 17, 2019
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If f(x) satisfies the conditions of Rolle’* theorem in [1, 2] and f(x) is continuous in [1, 2] , then ∫f'(x)dx for x ∈ [1, 2]
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Mar 16, 2019
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applications of derivatives
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Find the values of a for which all roots of the equation 3x^4 + 4x^3 – 12x^2 + a = 0 are real and distinct.
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Mar 12, 2019
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the maxima and minima
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Let f be differentiable for all x. If f(1) = – 2 and f'(x) ≥ 2 for all x ∈ [1, 6] then show that f(6) ≥ 8
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Mar 11, 2019
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If f(x) and g(x) are continuous in [a, b] and differentiable in (a, b), show that there exists some c ∈ (a, b) such that
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Mar 8, 2019
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rolles theorem
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If the equation (x/(1 + x^2)^2 + a(x/(1 + x^2) + 3 = 0 has exactly two real roots which are distinct, then the set of possible real values of a is
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Mar 7, 2019
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If the function f (x) = ax^3 + bx^2 + 11x - 6 satisfies the condition of Rolle'* theorem in [1, 3] and f'(2 + 1/√3) = 0
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Mar 1, 2019
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applications of derivatives
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If the function f(x) = x^3 – 6x^2 + ax + b is defined on [1, 3] satisfies the hypothesis of Rolle’* theorem, then find the values of a and b.
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Feb 27, 2019
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Let r, * and t be the roots of the equation, 8x^3 + 1001x + 2008 = 0.
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Feb 26, 2019
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If the value of c prescribed in the Rolle’* theorem for the function f(x) = 2x(x – 3)^n, n ∈ N on [0, 3] is 3/4, then find the value of n.
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Feb 26, 2019
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Find the roots of x^2 +6c -(a^2u200bu200bu200bu200bu200bu200bu200b +2a -8) = 0
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Feb 16, 2019
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algebraic expressions
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If 2a + 3b + 6c = 0, then prove that at least one root of the equation ax^2 + bx + c = 0 **** in the interval (0, 1).
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Feb 14, 2019
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differential calculus
rolles theorem
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quadratic equations
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complex numbers
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Verify Rolle’* theorem for the function f(x) = x^3 – 3x^2 + 2x + 5 on [0, 2].
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Feb 13, 2019
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The number of distinct real roots of x^4 – 4x^3 + 12x^2 + x – 1 = 0 is ...
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Feb 9, 2019
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rolles theorem
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lagranges mean value theorem
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Let r, * and t be the roots of the equation, 8x^3 + 1001x + 2008 = 0.
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Feb 2, 2019
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rolles theorem
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quadratic equations
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lagranges mean value theorem
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In [0, 1] Lagranges Mean Value Theorem is not applicable to (a) f(x) = {((1/2 - x), " x < 1/2), ((1/2 - x)^2, x ≥ 1/2)
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Jan 30, 2019
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rolles theorem
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(4D^4 - 4D^3 - 23D^2 + 12D + 36)y =0
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Jan 28, 2019
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differential equations
class-12
jee mains
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lagranges mean value theorem
rolles theorem
optics
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If f(x) = ∫e^t^2(t – 2)(t – 3) for t ∈ [0, x] for all x > 0 then (a) f has a local maximum at x = 2 (b) f is decreasing on (2, 3)
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Jan 16, 2019
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rolles theorem
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