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mathematics
calculus 6th edition

Questions and Answers of Calculus 6th edition

Find the derivative of the function.y = 101–x2
Differentiate.f(x) = x/(x +c/x)
Differentiate the function.y = 4π2
Find the derivative of the function.F(z) = √z –1/√z + 1
Differentiate.f(x) = ax + b/cx + d
Differentiate the function.g(u) = √2u + √3u
Find the derivative of the function.G(y) = (y – 1)4/(y2 + 2y)5
Differentiate the function.H(x) = (x + x–1)3
Find the derivative of the function.y = r/√r2 + 1
Find the derivative of the function.y = eu – e–u/eu + e–u
Differentiate the function.u = 5√t + 4√t5
Find the derivative of the function.G(y) = (y2/y + 1)5
Find the derivative of the function.y = 2sin π x
Find an equation of the tangent line to the given curve at the specified point.y = ex/x, (1, e)
Differentiate the function.y = ex+1 + 1
Find the derivative of the function.y = tan2(3θ)
Find the derivative of the function.y = sec2x + tan2x
Find the derivative of the function. t f(t)= 2 √² + 4
Find the derivative of the function.y = x sin 1/x
Find the derivative of the function.y = cos(1 – e2x/1 + e2x)
Find the limit. lim sin 3x X
(a) If f(x) = x/(x2 – 1), find f'(x). (b) Check to see that your answer to part (a) is reasonable by comparing the graphs of f and f'.
Find the derivative of the function.y = ek tan√x
(a) If f(x) = (x – 1)ex. find f'(x) and f"(x). (b) Check to see that your answers to part (a) are reasonable by comparing the graphs of f, f', and f".
Find the limit. sin 4x lim x-0 sin 6x
Find the derivative of the function.f(t) = tan(et) + etan t
Find the limit. tan 6t lim 1-0 sin 2t
(a) If f(x) = x/(x2 + 1), find f'(x) and f"(x). (b) Check to see that your answers to part (a) are reasonable by comparing the graphs of f, f', and f".
Find the limit. lim 8-0 cos - 1 sin 0
Find the derivative of the function.y = sin(sin(sin x))
Find the derivative of the function. y = √√√x + √√√√x + √√√x
Find the limit. lim 8-0 sin(cos () sec
If g(x) = x/ex, find g(n)(x).
Find the limit. lim 1-0 sin² 3t
Find the derivative of the function.g(x) = (2rarx + n)P
Find the limit. lim 800 sin 0 tan 0
Find the limit. lim x-0 sin(x²) X
Find the derivative of the function.y = 23x2
Find the limit. 1 - tan x lim #→#/4 sin x cos x
Find the derivative of the function.y = [x + (x + sin2x3)]4
Find the first and second derivatives of the function.h(x) = √x2 + 1
Find the limit. sin(x - 1) lim 2 x1x² + x - 2
Find the first and second derivatives of the function.y = xeex
Find the first and second derivatives of the function.y = eαx sin βx
Find the first and second derivatives of the function.y = eex
Find an equation of the tangent line to the curve at the given point.y = (1 + 2x)10, (0, 1)
Find an equation of the tangent line to the curve at the given point.y = sin x + sin2x, (0,0)
Find an equation of the tangent line to the curve at the given point.y = x2e–x, (1, 1/e)
Find an equation of the tangent line to the curve y = x√x that is parallel to the line y = 1 + 3x.
If F(x) = f(xf(xf(x))), where f(1) = 2,f(2) = 3, f'(1) = 4, f'(2) = 5, and f'(3) = 6, find F'(1).
Show that the function y = Ae–x + Bxe–x satisfies the differential equation y´´ + 2y´ + y = 0.
Differentiate the function.f(t) = 1/2t6 – 3t4 + 1
Find the derivative of the function.F(x)= (4x – x2)100
Differentiate.y = eu (cos u + cu)
Differentiate.V(x) = (2x3 + 3)(x4 – 2x)
Differentiate the function.f(t) = 3/4(t4 + 8)
Find the derivative of the function.F(x) = 4√1 + 2x + x3
Differentiate.y = x/2 – tan x
Find the exact value of each expression.(a) tan–1(1/√3) (b) sec–1 2
The number N (in millions) of cellular phone subscribers worldwide is shown in the table. (Midyear estimates are given.)(a) Use the data to sketch a rough graph of N as a function of(b) Use your
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.tan–1 x = sin–1x /cos–1x
Find a formula for the inverse of the function.y = ex/(1 + 2ex)
Find the functions (a) f ∘ g, (b) g ∘ f, (c) f ∘ f, and (d) g ∘ gand their domains. f(x) X 1 + x' g(x) = sin 2x
Use a graphing calculator or computer to determine which of the given viewing rectangles produces the most appropriate graph of the function f(x) = x4 – 16x2 + 20.(a) [–3, 3] by [–3, 3] (b)
Sketch the graph of the function g(x) = |x2 – 1| –|x2 – 4].
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f and g are functions, then f ∘ g = g
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is one-to-one, then f–1(x) = 1/f(x).
Determine an appropriate viewing rectangle for the given function and use it to draw the graph.f(x) = cos(0.001x)
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If x > 0 and a > 1, then In x/In a = In x/a.
Determine an appropriate viewing rectangle for the given function and use it to draw the graph.f(x) = sin √x
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.tan–1(–1) = 3π/4
Determine an appropriate viewing rectangle for the given function and use it to draw the graph.y = 10 sin x + sin 100x
Find the functions (a) f ∘ g, (b) g ∘ f, (c) f ∘ f, and (d) g ∘ gand their domains. f(x)=√x, g(x)=√1 - x
Find the functions (a) f ∘ g, (b) g ∘ f, (c) f ∘ f, and (d) g ∘ gand their domains.f(x) = x – 2, g(x) = x2 + 3x + 4
Find the functions (a) f ∘ g, (b) g ∘ f, (c) f ∘ f, and (d) g ∘ gand their domains. f(x) = x + - 1 g(x) = x + x + 2
Find the functions (a) f ∘ g, (b) g ∘ f, (c) f ∘ f, and (d) g ∘ gand their domains.f(x) = 1 – 3x, g(x) = cos x
Find the exact value of each expression.(a) arctan 1 (b) sin–1(1/√2)
Express the given quantity as a single logarithm.ln(a + b) + ln(a – b) – 2 ln c
Find the exact value of each expression.(a) tan(arctan 10) (b) sin–1(sin(7π/3))
Find the exact value of each expression.(a) tan(sec–1 4) (b) sin(2 sin–1(3/5))
Find the exact value of each expression.(a) cot–1(–√3) (b) arccos(-1/2)
Suppose f is even and g is odd. What can you say about fg?

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