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mathematics
precalculus

Questions and Answers of Precalculus

Find the function f such that f '(x) = x f (x) - x and f (0) = 2.
Find an equation of the curve that passes through the point (0, 2) and whose slope at (x, y) is x/y.
Find the solution of the differential equation that satisfies the given initial condition.dL/dt = kL2In t, L(1) = -1
Find the solution of the differential equation that satisfies the given initial condition.y' tan x = a + y, y(π/3) = a, 0 < x < π/2
Find the solution of the differential equation that satisfies the given initial condition.dP/dt = √Pt, P(1) = 2
Find the solution of the differential equation that satisfies the given initial condition.x In x =y(1 + √3 + y2)y', y(1) = 1
Find the solution of the differential equation that satisfies the given initial condition.x + 3y2 √x2 + 1 dy/dx = 0, y = (0) = 1
Find the solution of the differential equation that satisfies the given initial condition.du/dt = 2t + sec2t/2u, u(0) = -5
Match the differential equation with its direction field (labeled I–IV). Give reasons for your answer.y' = sin x sin y II I IV -- -- -- II -- -- -- -2 1. /// ///! ///1|I\ ///||\\ ///||\ ////
Prove Formulas 9.
If ∫90 f(x) dx = 37 and ∫90 g(x) dx = 16, find ∫90 [2f(x) + 3g(x)] dx
Find dy/dx by implicit differentiation.x3 - xy2 + y3 = 1
Find the derivative of the function.f (θ) = cos(θ2)
Find the derivative of the function.f (x) = 1/ 3√x2 - 1
Find the derivative of the function.f (x) = √5x + 1
Find the derivative of the function.F(x) = (1 + x + x2)99
Differentiate.f(θ) = sin (θ)/1 + cos (θ)
Differentiate.y = sin θ cos θ
Differentiate.f (x) = ex cos x
Differentiate.f (x) = x cos x + 2 tan x
Evaluate the integral. sin o coso
Use Exercise 52 to find ∫ x4ex dx.
Use Exercise 51 to find ∫ (ln x)3 dx.
Evaluate the integral. dx (x + 1)?
Evaluate the integral. (х + 1)? dx х
Suppose that |x - 2| < 0.01 and |y - 3| , 0.04. Use the Triangle Inequality to show that |(x + y) - 5| < 0.05.
Solve for x, assuming a, b, and c are negative constants.ax + b/c < b
Solve for x, assuming a, b, and c are negative constants.ax + b < c
Solve for x, assuming a, b, and c are positive constants.a < bx + c < 2a
Solve for x, assuming a, b, and c are positive constants.a(bx - c) > bc
Solve the inequality.|5x - 2 | < 6
Solve the inequality.1 < |x| < 4
Solve the inequality.0 < |x -5 | < 1/2
Solve the inequality.|x - 6| < 0.1
Solve the inequality.|2x - 3| < 0.4
Solve the inequality.|x + 1 | > 3
Solve the inequality.|x + 5| > 2
Solve the inequality.|x - 4 | < 1
Solve the inequality.|x | > 3
Solve the inequality.|x | < 3
Solve the equation for x.|2x - 1/x + 1| = 3
Solve the equation for x.|x + 3| = |2x + 1|
Solve the equation for x.|3x + 5 | = 1
Solve the equation for x.|2x| = 3
If a ball is thrown upward from the top of a building 128 ft high with an initial velocity of 16 ft/s, then the height h above the ground t seconds later will be h = 128 + 16t - 16t2During what
As dry air moves upward, it expands and in so doing cools at a rate of about 1°C for each 100-m rise, up to about 12 km.(a) If the ground temperature is 20°C, write a formula for the temperature at
The relationship between the Celsius and Fahrenheit temperature scales is given by C = 5/9 (F - 32), where C is the temperature in degrees Celsius and F is the temperature in degrees Fahrenheit. What
Use the relationship between C and F given in Exercise 39 to find the interval on the Fahrenheit scale corresponding to the temperature range 20 < C < 30.
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.-3 < 1/x < 1
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.(x + 1)(x - 2)(x + 3) > 0
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.1/x < 4
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x3 + 3x < 4x2
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x3 > x
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x3 - x2 < 0
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x2 > 5
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x2 < 3
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x2 + x > 1
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x2 + x + 1 > 0
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.x2 < 2x + 8
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.2x2 + x < 1
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.(2x + 3)(x - 1) > 0
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.(x - 1)(x - 2) > 0
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.2x - 3 , x + 4 , 3x - 2
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.4x , 2x + 1 < 3x + 2
Solve the inequality in terms of intervals and illustrate the solution set on the real number line. -5 < 3 - 2x < 9
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.0 < 1 - x < 1
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.-1 < 2x - 5 < 7
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.1 < 3x + 4 < 16
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.1 + 5x . 5 - 3x
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.2x + 1< 5x - 8
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.4 - 3x > 6
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.1 - x < 2
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.3x - 11 < 4
Solve the inequality in terms of intervals and illustrate the solution set on the real number line.2x + 7 > 3
Rewrite the expression without using the absolute-value symbol.|1 - 2x2 |
Rewrite the expression without using the absolute-value symbol.|x2 + 1|
Rewrite the expression without using the absolute-value symbol.|2x - 1|
Rewrite the expression without using the absolute-value symbol.|x + 1 |
Rewrite the expression without using the absolute-value symbol.|x - 2 | if x > 2
Rewrite the expression without using the absolute-value symbol.|x - 2 | if x < 2
Rewrite the expression without using the absolute-value symbol.||-2 | - |-3 ||
Rewrite the expression without using the absolute-value symbol.|√5 - 5|
Rewrite the expression without using the absolute-value symbol.|π - 2 |
Rewrite the expression without using the absolute-value symbol.|-π |
Rewrite the expression without using the absolute-value symbol.|5 | - |-23 |
Rewrite the expression without using the absolute-value symbol.|5 - 23 |
A spring with a mass of 2 kg has damping constant 16, and a force of 12.8 N keeps the spring stretched 0.2 m beyond its natural length. Find the position of the mass at time t if it starts at the
A series circuit contains a resistor with R = 40 V, an inductor with L = 2 H, a capacitor with C = 0.0025 F, and a 12-V battery. The initial charge is Q = 0.01 C and the initial current is 0. Find
Use power series to solve the differential equation y'' - xy' - 2y = 0
Use power series to solve the initial-value problemy'' + xy' + y = 0, y(0) = 0 y'(0) = 1
Solve the boundary-value problem, if possible.y'' + 4y' + 29y = 0, y(0) = 1, y(π) = 2e-2π
Solve the boundary-value problem, if possible.y'' + 4y' + 29y = 0, y(0) = 1, y(π) = -1
Solve the initial-value problem.9y'' + y = 3x + e-x, y(0) = 1, y'(0) = 2
Solve the initial-value problem.y'' - 5y' + 4y = 0, y(0) = 0, y'(0) = 1
Solve the initial-value problem.y'' - 6y' + 25y = 0, y(0) = 2, y'(0) = 1
Solve the initial-value problem.y'' + 6y' = 0, y(1) = 3, y'(1) = 12
Solve the differential equation.d2y/dx2 + y = csc x, 0 < x < π/2
Solve the differential equation.d2y/dx2 - dy/dx - 6y = 1 + e-2x
Solve the differential equation.d2y/dx2 + 4y = sin 2x
Solve the differential equation.d2y/dx2 - 2 dy/dx + y = x cos x

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