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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.f(x) = 5 – 12x + 3x2, [1,3]
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.f(x) = x3 – x2 – 6x + 2,
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.f(x) = cos 2x, [π/8, 7π/8]
Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.f(x) = √x –1/3x, [0,9]
Find the critical numbers of the function.f(x) = x2e–3x
Find the critical numbers of the function.g(x) = x1/3 – x–2/3
Find the critical numbers of the function.g(x) = √1 – x2
Find the critical numbers of the function.h(p) = p – 1/p2 + 4
Find the critical numbers of the function.s(t) = 3t4 + 4t3 – 6t2
Find the critical numbers of the function.f(x) = x3 + x2 + x
Find the critical numbers of the function.f(x) = x3 + 3x2 – 24x
Find the critical numbers of the function.f(x) = x3 + x2 – x
Find the critical numbers of the function.f(x) = 5x2 + 4x
Sketch the graph of a function f that is continuous on [1, 5] and has the given properties.f has no local maximum or minimum, but 2 and 4 are critical numbers
Calculate y´. y = (x4 + 3x2 + 5)3
Calculate y´.y = cos(tan x)
Calculate y´.y = √x + 1/3√x4
Calculate y´.y = 3x – 2/√2x + 1
Calculate y´.y = 2x√x2 + 1
Calculate y´.y = ex/1 + x2
Calculate y´.y = esin 2θ
Calculate y´.y = e–t(t2 – 2t + 2)
Calculate y´.y = t/1 – t2
Calculate y´.y = √x cos √x
Calculate y´.y = e1/x/x2
Calculate y´.y = 1/sin(x – sin x)
Evaluate lim x-0 sin(3 + x)² - sin 9 X
Calculate y´.xy4 + x2y = x + 3y
Calculate y´.y = ln(csc 5x)
Calculate y´.y = sec 2θ/1 + tan 2θ
Calculate y´.x2 cos y + sin 2y = xy
Calculate y´.y = ecx (c sin x – cos x)
Calculate y´.y = ln(x2ex)
Calculate y´.y = 3x ln x
Calculate y´.y = sec (1 + x2)
Calculate y´. y=1/√√x + √√√x
Calculate y´.y = (1 – x–1)–1
Calculate y´. y = √sin sin √x
Calculate y´.sin(xy) = x2 – y
Calculate y´.y = log5(1 + 2x)
Calculate y´.y = (cos x)2
Calculate y´.y = (x2 + 1)4/(2x + 1)3(3x – 1)5
Calculate y´.y = x tan–1(4x)
Calculate y´.y = ecos x + cos(ex)
Calculate y´.y = 10tan πθ
Calculate y´.y = √t ln(t4)
Calculate y´.y = arctan(arcsin √x).
Calculate y´.y = tan2 (sin θ)
Calculate y´.xey = y – 1
Calculate y´.y = √x + 1 (2 – x)5/(x + 3)7
Calculate y´.y = (x + λ)4/x4 + λ4
Calculate y´.y = x sinh(x2)
Calculate y´. y = ln x² - 4 2x + 5
Calculate y´.y = sin mx/x
Calculate y´.y = x tanh–1 √x
Calculate y´.y = sin2(cos/√sin πx)
Find f(n)(x) if f(x) = 1/(2 – x).
Prove the identity.cosh x + sinh x = ex
Prove the identity.cosh x – sinh x = e–x
Prove the identity.coth2x – 1 = csch2x
Prove the identity.cosh 2x = cosh2x + sinh2x
Prove the identity.tanh(ln x) x2 – 1/x2 + 1
Find the derivative. Simplify where possible.f(x) = tanh(1 + e2x)
Find the derivative. Simplify where possible.g(x) = cosh(lnx)
Find the derivative. Simplify where possible.y = x coth(1 + x2)
Find the derivative. Simplify where possible.f(t) = csch t(1 – In csch t)
Find the derivative. Simplify where possible.f(t) = sech2(et)
Find the derivative. Simplify where possible. 1+tanh.x V1 −tanh.x 4 y =
Find the derivative. Simplify where possible.y = sinh(cosh x)
Find the derivative. Simplify where possible.y = arctan(tanh x)
Find the derivative. Simplify where possible.G(x) = 1 – cosh x/1 + cosh x
Find the derivative. Simplify where possible.y = x2 sinh–1(2x)
Find the derivative. Simplify where possible.y = tanh–1√x
Find the derivative. Simplify where possible.y = sech–1√1 – x2, x > 0
Find the derivative. Simplify where possible.y = coth–1√x2 + 1
The cost function for production of a commodity is C(x) = 339 + 25x – 0.09x2 + 0.0004x3 (a) Find and interpret C'(100). (b) Compare C'(100) with the cost of producing the 101st item.
If y = x3 + 2x and dx/dt = 5, find dy/dt when x = 2.
A particle moves along the curve y = √1 + x3. As it reaches the point (2, 3), the y-coordinate is increasing at a rate of 4 cm/s. How fast is the x-coordinate of the point changing at that instant?
Find the linearization L(x) of the function at a.f(x) = x3/4, a = 16
Find the differential of each function.(a) y = s/(1+ 2s) (b) y = e–ucos u
Find the differential of each function.(a) y = u + 1/u –1 (b) y = (1 + r3)–2
Find the differential of each function.(a) y = etan π t (b) y = √1 + ln z
Differentiate the function.f(x) = ln(x2 + 10)
Differentiate the function.f(x) = ln(sin2 x)
Differentiate the function.f(x) = log2(1– 3x)
Differentiate the function.f(x) = log5(xex)
Differentiate the function.f(x) = 5√In x
Differentiate the function.f(x) = ln 5√x
Differentiate the function.f(x) = sin x ln(5x)
Differentiate the function.f(t) = 1 + ln t/1 – In t
Differentiate the function.F(t) = ln (2t + 1)3/(3t – 1)4
Differentiate the function.h(x) = ln(x + √x2 – 1).
Differentiate the function.g(x) = ln(x√x2 – 1)
Differentiate the function.F(y) = y ln(1 + ey)
Differentiate the function.f(u) = In u/1 + ln(2u)
Differentiate the function.y = 1/In x
Differentiate the function.y = ln|2 – x – 5x2|
Differentiate the function.y = ln(e–x + xe–x)
Differentiate the function.y = [ln(1 + ex)]2
Differentiate the function.y = 2x log10√x

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