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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises complete the table for the radioactive isotope. Isotope = 226Ra Amount Amount After Half-life Initial (in years) Quantity 1000 Years 1599 After 10,000 Years 0.1 g
In Exercises some of the curves corresponding to different values of C in the general solution of the differential equation are shown in the graph. Find the particular solution that passes through
In Exercises some of the curves corresponding to different values of C in the general solution of the differential equation are shown in the graph. Find the particular solution that passes through
In Exercises complete the table for the radioactive isotope. Half-life Initial Isotope (in years) Quantity 226Ra 1599 Amount After 1000 Years 1.5 g Amount After 10,000 Years
In Exercises find all functions ƒ having the indicated property.All tangents to the graph of ƒ pass through the origin.
In Exercises find all functions ƒ having the indicated property.The tangent to the graph of ƒ at the point (x, y) intersects thex-axis at (x + 2, 0).
In Exercises some of the curves corresponding to different values of C in the general solution of the differential equation are shown in the graph. Find the particular solution that passes through
In Exercises complete the table for the radioactive isotope. Half-life Initial Isotope (in years) Quantity 226Ra 1599 20 g Amount After 1000 Years Amount After 10,000 Years
In Exercises determine the quadrants in which the solution of the differential equation is an increasing function. Explain. dy dx || 1 2x²y
In Exercises determine the quadrants in which the solution of the differential equation is an increasing function. Explain. dy 1 dx 2xy
In Exercises find an equation of the graph that passes through the point and has the given slope. (8,2), y': = 20 3x
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = x²ex - 5x²
In Exercises find an equation of the graph that passes through the point and has the given slope. (9, 1), y'= 2x
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = ln x
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = cos x
In Exercises find an equation of the graph that passes through the point and has the given slope. (0, 2), y' = X 4y
In Exercises find an equation of the graph that passes through the point and has the given slope. (1, 1), y'= 9x 16y
In Exercises find the exponential function y = Cekt that passes through the two given points. 5 4 3 2 1 برا y (4, 5) (3,1) + 12 3 4 5 t
Give the differential equation that models exponential growth and decay.
In Exercises find the particular solution that satisfies the initial condition. Differential Equation dP - kP dt = 0 Initial Condition P(0) = Po
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = sin x
In Exercises find the particular solution that satisfies the initial condition. Differential Equation dTk(T70) dt = 0 Initial Condition T(0) = 140
Describe what the values of C and in the exponential growth and decay model, k represent y = Cekt.
In Exercises find the exponential function y = Cekt that passes through the two given points. 3 2 1 y (0,4) 1 2 3 نرا 4 (5,-/-) ► t 5
In Exercises find the exponential function y = Cekt that passes through the two given points. 654 4 32 2 1 y (1,5) (5,2) H H 1 2 3 4 5 6 1
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = x²(2 + ex)
In Exercises find the exponential function y = Cekt that passes through the two given points. 5 4 3 2 (o,) (5,5) + + 12 3 4 5 t
In Exercises find the particular solution that satisfies the initial condition. Differential Equation dr ds er-2s Initial Condition r(0) = 0
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = x²ex
In Exercises find the particular solution that satisfies the initial condition. Differential Equation du dv uv sin v² Initial Condition u(0) = 1
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = x³
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0. y = C₁e²x + C₂e-2x + C3 sin 2x + C₂ cos 2x
In Exercises determine whether the function is a solution of the differential equation xy' - 2y = x³ex.y = x2
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = 3e2x - 4 sin 2x
In Exercises find the particular solution that satisfies the initial condition. Differential Equation y√1-x²y' - x√1 - y² = 0 Initial Condition y(0) = 1
In Exercises write and solve the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable.The rate of change of N is
In Exercises find the particular solution that satisfies the initial condition. Differential Equation y(1+x²)y' x(1 + y²) = 0 Initial Condition y(0)=√√√3
In Exercises find the particular solution that satisfies the initial condition. Differential Equation 2xy' - In x² = 0 Initial Condition y(1) = 2
In Exercises find the function y = ƒ(t) passing through the point (0, 10) with the given first derivative. Use a graphing utility to graph the solution. dy dt || 3 4 y
In Exercises find the function y = ƒ(t) passing through the point (0, 10) with the given first derivative. Use a graphing utility to graph the solution. dy dt || 1 2 y
In Exercises write and solve the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable.The rate of change of P is
In Exercises find the particular solution that satisfies the initial condition. Differential Equation y(x + 1) + y = 0 Initial Condition y(-2) = 1
In Exercises find the function y = ƒ(t) passing through the point (0, 10) with thegiven first derivative. Use a graphing utility to graph the solution. dy dt || 2
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = 5 ln x
In Exercises find the particular solution that satisfies the initial condition. Differential Equation √x + √yy' = 0 Initial Condition y(1) = 9
In Exercises find the particular solution that satisfies the initial condition. Differential Equation yy' - 2e* = 0 Initial Condition y(0) = 3
In Exercises find the function y = ƒ(t) passing through the point (0, 10) with the given first derivative. Use a graphing utility to graph the solution. dy = dt -9√t
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = e-2x
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = 3 sin 2x
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the
In Exercises find the general solution of the differential equation. x² 16y' 11x - =
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = 3 cos 2x
In Exercises verify the particular solution of the differential equation. Solution y = e-cos.x Differential Equation and Initial Condition y' = y sin x (7) 2 y = 1
In Exercises find the general solution of the differential equation. √1 - 4x² y' = x
In Exercises find the general solution of the differential equation.12yy' - 7ex = 0
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = 2 sin x
In Exercises find the general solution of the differential equation.y ln x - xy' = 0
In Exercises determine whether the function is a solution of the differential equation y(4) - 16y = 0.y = 3 cos x
In Exercises verify the particular solution of the differential equation. Solution y = 4e-6x² Differential Equation and Initial Condition y' = -12xy y(0) = 4
In Exercises write and solve the differential equation that models the verbal statement.The rate of change of P with respect to t is proportional to 25 - t.
In Exercises verify the particular solution of the differential equation. Solution y = 6x- - 4 sin x + 1. - Differential Equation and Initial Condition y' = 6 - 4 cos x y(0) = 1
In Exercises verify the solution of the differential equation. Solution y = (e-4x + ex) Differential Equation y" + 4y = 2et
In Exercises write and solve the differential equation that models the verbal statement.The rate of change of Q with respect to t is inversely proportional to the square of t.
In Exercises verify the particular solution of the differential equation. Solution y = sin x cos x - cos² x Differential Equation and Initial Condition 2y + y' = 2 sin(2x) - 1 y TT = 0
In Exercises verify the solution of the differential equation. Solution y = -cos x In|sec x + tan x| Differential Equation y" + y = tan x
In Exercises find the general solution of the differential equation. yy' = -8 cos(πX)
In Exercises solve the differential equation. y' = √xy
In Exercises find the general solution of the differential equation. dr ds 0.75s
In Exercises solve the differential equation.xy + y = 100x
In Exercises find the general solution of the differential equation.yy' = 4 sin x
In Exercises solve the differential equation. y X 4y
In Exercises solve the differential equation.(1 + x²)y' - 2xy = 0
In Exercises find the general solution of the differential equation. dr ds 0.75r
In Exercises find the general solution of the differential equation.xy' = y
In Exercises verify the solution of the differential equation. Solution y = C₁ sin x C₂ cos x - Differential Equation y" + y = 0
In Exercises solve the differential equation. y' || 5x y
In Exercises verify the solution of the differential equation. Solution y = C₁e* cos x + C₂ex sin x Differential Equation y" + 2y + 2y = 0
In Exercises solve the differential equation.y' = x(1 + y)
In Exercises find the general solution of the differential equation. dy dx X - 9 2y3
In Exercises find the general solution of the differential equation.(2 + x)y' = Зу
In Exercises verify the solution of the differential equation. Solution y² - 2 ln y = x² Differential Equation dy xy dx = y²-1
In Exercises solve the differential equation. dy dx || 6-y
In Exercises find the general solution of the differential equation. dy dx x² + 5y- = 0
In Exercises find the general solution of the differential equation. dy dx 3x² y²
In Exercises verify the solution of the differential equation. Solution y = e-2r Differential Equation 3y + 5y = -e-2x
In Exercises verify the solution of the differential equation. Solution x² + y² = Cy Differential Equation 2xy x² - y² y =
In Exercises solve the differential equation. dy dx = 5 - 8x
In Exercises solve the differential equation. dy dx = y + 3
In Exercises verify the solution of the differential equation. Solution y = Ce4x Differential Equation y' = 4y
In Exercises find the general solution of the differential equation. y || xp X Ap
In Exercises solve the differential equation. dy dx = x + 3
Prove that * (I + zk^^ + ¹)U[ = 11
Prove that tanh-1x - 1/2 in (1 + x). In -1 < x < 1.
In Exercises evaluate the definite integral using the formulas from Theorem 5.20.Data from in Theorem 5.20 THEOREM 5.20 Differentiation and Integration Involving Inverse Hyperbolic Functions Let u be
In Exercises evaluate the definite integral using the formulas from Theorem 5.20.Data from in Theorem 5.20 THEOREM 5.20 Differentiation and Integration Involving Inverse Hyperbolic Functions Let u be
In Exercises find the area of the region. y = -2 4- x √4x² -1 4 3- نرا 2 y - + 1 2 X
In Exercises evaluate the definite integral using the formulas from Theorem 5.20.Data from in Theorem 5.20 THEOREM 5.20 Differentiation and Integration Involving Inverse Hyperbolic Functions Let u be
In Exercises find the area of the region. y 0.5 0.4 0.3 0.2 0.1 1 6 16 + x² 1 2 3 نرا + 4 5 X
In Exercises evaluate the definite integral using the formulas from Theorem 5.20.Data from in Theorem 5.20 THEOREM 5.20 Differentiation and Integration Involving Inverse Hyperbolic Functions Let u be

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