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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

(a) Graph the function ƒ(x) = arccos x + arcsin x on the interval [-1, 1].(b) Describe the graph of ƒ.(c) Verify the result of part (b) analytically.
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. Because cos TT 3 = 2' it follows that arccos 2 = ગંગ 3°
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.arcsin² x + arccos²x = 1
The graphs of ƒ(x) = sin x and g(x) = cos x are shown below.(a) Explain whether the pointslie on the graph of y = arcsin x.(b) Explain whether the pointslie on the graph of y = arcos x. f(x) = sin
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.d/dx[arctan(tan x)] = 1 for all x in the domain.
In Exercises use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point. arctan(x + y) = y² + (1,0)
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The range of y = arcsin x is [0, π].
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The slope of the graph of the inverse tangent function is positive
In Exercises analyze and sketch a graph of the function. Identify any relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = arccos X 4
In Exercises use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point. arcsin x + arcsin y 2 法(图) 2 2
(a) Use a graphing utility to evaluate arcsin(arcsin 0.5) and arcsin(arcsin 1).(b) Letƒ(x) = arcsin(arcsin x).Find the values of x in the interval - 1 ≤ x ≤ 1 such thatƒ(x) is a real number.
In Exercises analyze and sketch a graph of the function. Identify any relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = arctan x + EN 2
In Exercises use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point. x² + x arctan y = y - 1, 4,1)
Explain why tan π = 0 does not imply that arctan 0 = π.
Explain why the domains of the trigonometric functions are restricted when finding the inverse trigonometric functions.
In Exercises use implicit differentiation to find an equation of the tangent line to the graph of the equation at the given point.arctan(xy) = arcsin(x + y), (0, 0)
In Exercises use a computer algebra system to find the linear approximationand the quadratic approximationof the function ƒ at x = a. Sketch the graph of the function and its linear and quadratic
In Exercises analyze and sketch a graph of the function. Identify any relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.ƒ(x)= arcsec 2x
In Exercises use a computer algebra system to find the linear approximationand the quadratic approximationof the function ƒ at x = a. Sketch the graph of the function and its linear and quadratic
In Exercises analyze and sketch a graph of the function. Identify any relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results.ƒ(x) = arcsin(x - 1)
In Exercises find any relative extrema of the function.h(x) = arcsin x − 2 arctan x
In Exercises use a computer algebra system to find the linear approximationand the quadratic approximationof the function ƒ at x = a. Sketch the graph of the function and its linear and quadratic
In Exercises find any relative extrema of the function.ƒ(x) = arctan x - arctan(x – 4)
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = arcsec 4x, 2 ㅠ 44,
In Exercises use a computer algebra system to find the linear approximationand the quadratic approximationof the function ƒ at x = a. Sketch the graph of the function andits linear and quadratic
In Exercises find any relative extrema of the function.ƒ(x) = arcsin x − 2x
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = 3x arcsin X, 프4 ㅠ 24
In Exercises find any relative extrema of the function.ƒ(x) = arcsec x - x
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = 2 arcsin x, 1 TT 2' 3,
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = arctan 즐 2. 푸 4
In Exercises find an equation of the tangent line to the graph of the function at the given point. y || 1 - arccos x, 2 √√2 3T 28
In Exercises find the derivative of the function. y = 25 arcsin X 5 - x√25 - x²
In Exercises find the derivative of the function. y = 8 arcsin X 4 x 16x² 2
In Exercises find the derivative of the function. y = arctan X 2 1 2(x² + 4)
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = 4x arccos(x - 1), (1, 2π)
In Exercises find the derivative of the function. y = arctan x+ X 1 + x²
In Exercises find the derivative of the function. y = 1 [x√/4 arcsin()] x√4x²+4 arcsin
In Exercises find the derivative of the function. y || 1 In 22 x + 1 x - 1 + arctan x
In Exercises find the derivative of the function. t y = ln(t² + 4) - 11/12 arctan 2
In Exercises find the derivative of the function. y = x arctan 2x In(1 + 4x²)
In Exercises find the derivative of the function. y = x arcsin x +V1. 1-x²
In Exercises find the derivative of the function. y = 2x arccos x - 2√1-x²
In Exercises find the derivative of the function. f(x) = arctan√x
In Exercises find the derivative of the function. g (x) arcsin 3x X
In Exercises find the derivative of the function.ƒ(x) = arcsin x + arccos x
In Exercises find the derivative of the function.h(t) = sin (arccos t)
In Exercises find the derivative of the function.h(x) = x2 arctan 5x
In Exercises verify each identity.(a)(b) arccsc x = arcsin - x ≥ 1
In Exercises verify each identity.(a)(b) arcsin(-x) = arcsin x, x ≤ 1 —
In Exercises find the derivative of the function.ƒ(x) = arctan ex
In Exercises find the derivative of the function.ƒ(x)= arcsec 2x
In Exercises write the expression in algebraic form. cos arcsin x-h r
In Exercises find the derivative of the function.g(x) = 3 arccos x/2
In Exercises find the derivative of the function.ƒ(t) = arcsin t²
In Exercises find the derivative of the function.ƒ(x) = 2 arcsin (x - 1)
In Exercises write the expression in algebraic form. csc arctan /2
In Exercises solve the equation for x.arccos x = arcsec x
In Exercises write the expression in algebraic form. tan arcsec X 3
In Exercises solve the equation for x.arcsin √2x = arccos√x
In Exercises solve the equation for x.arctan(2x - 5) = -1
In Exercises evaluate each expression without using a calculator.(a)(b) sec| arctan 3 5,
In Exercises solve the equation for x.arcsin (3x - π) = 1/2
In Exercises evaluate each expression without using a calculator.(a)(b) cot| arcsin| (-2)]
In Exercises evaluate each expression without using a calculator.(a)(b) انداد tan arccos- 2
In Exercises write the expression in algebraic form.sec[arcsin(x - 1)]
In Exercises use the figure to write the expression in algebraic form given y = arccos x, where 0 < y < π/2.sec y y 1 X
In Exercises write the expression in algebraic form.cos(arccot x)
In Exercises use the figure to write the expression in algebraic form given y = arccos x, where 0 < y < π/2.cot y y 1 X
In Exercises write the expression in algebraic form.sin(arcsec x)
In Exercises evaluate each expression without using a calculator.(a)(b) sin arctan 3 4
In Exercises write the expression in algebraic form.sec(arctan 4x)
In Exercises use the figure to write the expression in algebraic form given y = arccos x, where 0 < y < π/2.csc y y 1 X
In Exercises write the expression in algebraic form.cos (arcsin 2x)
In Exercises use the figure to write the expression in algebraic form given y = arccos x, where 0 < y < π/2.cos y y 1 X
In Exercises use the figure to write the expression in algebraic form given y = arccos x, where 0 < y < π/2.sin y y 1 X
In Exercises use the figure to write the expression in algebraic form given y = arccos x, where 0 < y < π/2.tan y y 1 X
In Exercises use a calculator to approximate the value. Round your answer to two decimal places.arctan(–5)
In Exercises use a calculator to approximate the value. Round your answer to two decimal places.arcsec 1.269
In Exercises evaluate the expression without using a calculator. arctan 3 3
In Exercises use a calculator to approximate the value. Round your answer to two decimal places.arcsin(-0.39)
In Exercises use a calculator to approximate the value. Round your answer to two decimal places.arccos (-0.8)
In Exercises evaluate the expression without using a calculator. arccos 1/2 arccos /
In Exercises evaluate the expression without using a calculator.arcsec(-√2)
In Exercises evaluate the expression without using a calculator.arccsc(-√2)
In Exercises evaluate the expression without using a calculator. arcsin 1/2 arcsin/
In Exercises evaluate the expression without using a calculator.arccot(-√3)
In Exercises determine the missing coordinates of the points on the graph of the function. -3-2 元|2 元 6 九 y = arctan x 元14 1 23 (3)
In Exercises evaluate the expression without using a calculator.arccos 1
In Exercises evaluate the expression without using a calculator.arcsin 0
In Exercises determine the missing coordinates of the points on the graph of the function. 3π 4 1 I 2 y = arccos x G (1/₂_) 2 الله ايه X
In Exercises evaluate the expression without using a calculator.log2 1/8
In Exercises evaluate the expression without using a calculator.log27 9
In Exercises evaluate the expression without using a calculator.log7 1
In Exercises evaluate the expression without using a calculator.loga 1/a
In Exercises write the exponential equation as a logarithmic equation or vice versa.(a) 2³ = 8 (b) 3-1 = 1/3
In Exercises write the exponential equation as a logarithmic equation or vice versa.(a) log10 0.01= -2 (b) log0.5 8 = -3
In Exercises write the exponential equation as a logarithmic equation or vice versa.(a) 272/3 = 9(b) 163/4 = 8
In Exercises write the exponential equation as a logarithmic equation or vice versa.(a) log3 1/9 = -2(b) 491/2 = 7
In Exercises sketch the graph of the function by hand.y = 2x
In Exercises sketch the graph of the function by hand.y = 4x-1

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