X f'(x) 2 5 2.1 approximate 6 2.2 8 2.3 9 2.4 11 4. The function f is twice differentiable for x> 0 with f(2)=-4 and f'(2) = 14. Values of f', the derivative of f, are given for selected values of x in the table above. a. Write an equation for the tangent line to the graph of f at x = 2. Use this line to approximate f(2.4). b. Use the trapezoidal approximation with four subdivisions of equal length and values from the table to 2.4 2.4 •S f'(x) dx. Use the approximation for S₂ f'(x) dx to estimate the value of f(2.4). Show the 2 computations that lead to your answer. c. Use Euler's method, starting at x = 2 with two steps of equal size, to approximate f(2.4). Show the computations that lead to your answer.
X f'(x) 2 5 2.1 approximate 6 2.2 8 2.3 9 2.4 11 4. The function f is twice differentiable for x> 0 with f(2)=-4 and f'(2) = 14. Values of f', the derivative of f, are given for selected values of x in the table above. a. Write an equation for the tangent line to the graph of f at x = 2. Use this line to approximate f(2.4). b. Use the trapezoidal approximation with four subdivisions of equal length and values from the table to 2.4 2.4 •S f'(x) dx. Use the approximation for S₂ f'(x) dx to estimate the value of f(2.4). Show the 2 computations that lead to your answer. c. Use Euler's method, starting at x = 2 with two steps of equal size, to approximate f(2.4). Show the computations that lead to your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:X
f'(x)
2
approximate
2.1
2.4
Str
6
2.2
8
f'(x) dx. Use the approximation for
2.3
4. The function f is twice differentiable for x> 0 with f(2)= -4 and f'(2) = 14. Values of f', the derivative of f, are
given for selected values of x in the table above.
-2.4
9
a. Write an equation for the tangent line to the graph of f at x = 2. Use this line to approximate ƒ(2.4).
b. Use the trapezoidal approximation with four subdivisions of equal length and values from the table to
2.4
11
I
f'(x) dx to estimate the value of ƒ(2.4). Show the
2
computations that lead to your answer.
c. Use Euler's method, starting at x = 2 with two steps of equal size, to approximate f(2.4). Show the
computations that lead to your answer.
d. Write the second-degree Taylor polynomial for f about x = 2. Use the Taylor polynomial to approximate
ƒ(2.4).
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