Initial Value Problems
Solve the initial value problems in Exercises 89–92.
dy/dx = (𝓍 + 1/𝓍)² , y(1)= 1
- Ch. 1 - Functions155
- Ch. 2 - Limits and Continuity240
- Ch. 3 - Derivatives337
- Ch. 4 - Applications of Derivatives293
- Ch. 5 - Integrals41
- Ch. 6 - Applications of Definite Integrals25
- Ch. 7 - Transcendental Functions489
- Ch. 8 - Techniques of Integration398
- Ch. 9 - First-Order Differential Equations60
- Ch. 10 - Infinite Sequences and Series119
- Ch. 11 - Parametric Equations and Polar Coordinates58
Finding Indefinite Integrals
Find the indefinite integrals (most general antiderivatives) in Exercises 73–88. You may need to try a solution and then adjust your guess. Check your answers by differentiation.
∫ 1/( r + 5)²dr
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Initial Value Problems
Solve the initial value problems in Exercises 89–92.
d^3 r/dt^3 = - cos t; r''(0) = r'(0) = 0 , r(0) = -1
Finding Indefinite Integrals
Find the indefinite integrals (most general antiderivatives) in Exercises 73–88. You may need to try a solution and then adjust your guess. Check your answers by differentiation.
∫ sec² s/10 ds
Applications
Suppose that f(x) = d/dx (1 − √x) and g(x) = d/dx (x + 2).
Find:
∫f(x) dx
Checking Antiderivative Formulas
Right, or wrong? Say which for each formula and give a brief reason for each answer.
∫√(2x + 1) dx = √(x² + x +C)
Identifying Extrema
In Exercises 63 and 64, the graph of f' is given. Assume that f has domain (-2, 2).
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a. Either use the graph to determine which intervals f is increasing on and which intervals f is decreasing on, or explain why this information cannot be determined from the graph.