Linear and Quadratic Approximations The linear and quadratic approximations of a function f at x = a are P 1 ( x ) = f ' ( a ) ( x − a ) + f ( a ) and P 2 ( x ) = 1 2 f " ( a ) ( x − a ) 2 + f ' ( a ) ( x − a ) + f ( a ) In Exercises 55-58, (a) find the specified linear and quadratic approximations of f , and (b) use a graphing utility to graph f and the approximations. f ( x ) = arctan x , a = 0
Linear and Quadratic Approximations The linear and quadratic approximations of a function f at x = a are P 1 ( x ) = f ' ( a ) ( x − a ) + f ( a ) and P 2 ( x ) = 1 2 f " ( a ) ( x − a ) 2 + f ' ( a ) ( x − a ) + f ( a ) In Exercises 55-58, (a) find the specified linear and quadratic approximations of f , and (b) use a graphing utility to graph f and the approximations. f ( x ) = arctan x , a = 0
Solution Summary: The author explains how to find the linear and quadratic approximations of f.
Linear and Quadratic Approximations The linear and quadratic approximations of a function f at
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In Exercises 55-58, (a) find the specified linear and quadratic approximations of f, and (b) use a graphing utility to graph f and the approximations.
Differential Calculus:
1. Show or prove that the degree of the HDE is 6.
2.Derive the integrable functions(variable substitution).
3.Find the general solution.
Calculus
Use linear algebra to solve the system of differential equations with inital values x(0) = -2, x(0) = 3.
Numerical analysis
In five decimal places, find the smallest root of x3 − 4.5x2 + 1.3x + 8 = 0 using bisection or secant method with the interval [-2, 0].
Chapter 3 Solutions
Calculus: Early Transcendental Functions (MindTap Course List)
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