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Use the Taylor series of degree 5 about a = 0 for f(x) = sin x to approximate the following integral. [²²: a. First, calculate the Taylor series of degree 5 about a = 0 for sin x. P₁(x) = sin √x dr b. Now substitute √ in for a into the Taylor series you found in Part a. Ps(vz)= c. Replace the integrand, sin √, with P₁(√) from Part b. and compute this new integral to approximate the original integral. Round your answer to within three decimal places. 1.2 S sin √x dx ≈ · [¹²³ Ps(√x) dx =

Use the Taylor series of degree 5 about a = 0 for f(x) = sin x to approximate the following integral. [²²: a. First, calculate the Taylor series of degree 5 about a = 0 for sin x. P₁(x) = sin √x dr b. Now substitute √ in for a into the Taylor series you found in Part a. Ps(vz)= c. Replace the integrand, sin √, with P₁(√) from Part b. and compute this new integral to approximate the original integral. Round your answer to within three decimal places. 1.2 S sin √x dx ≈ · [¹²³ Ps(√x) dx =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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l8 and l9  solve both please

Use the Taylor series of degree 5 about a = 0 for f(x) = sin x to approximate the following integral. 1.2 ft sin √z dz a. First, calculate the Taylor series of degree 5 about a = 0 for sin x. P₁(x)= b. Now substitute √ in for a into the Taylor series you found in part a. Ps(v)= c. Replace the integrand, sin √x, with P₁(√x) from Part b. and compute this new integral to approximate the original integral. Round your answer to within three decimal places. 1.2 [.. sin √x dx ≈ -1.2 [¹² P₁(√x) dx =
Transcribed Image Text:Use the Taylor series of degree 5 about a = 0 for f(x) = sin x to approximate the following integral. 1.2 ft sin √z dz a. First, calculate the Taylor series of degree 5 about a = 0 for sin x. P₁(x)= b. Now substitute √ in for a into the Taylor series you found in part a. Ps(v)= c. Replace the integrand, sin √x, with P₁(√x) from Part b. and compute this new integral to approximate the original integral. Round your answer to within three decimal places. 1.2 [.. sin √x dx ≈ -1.2 [¹² P₁(√x) dx =
A car is moving with speed 35 m/s and acceleration 3 m/s² at the given instant. Using a second-degree Taylor polynomial, estimate how far the car moves in the next second. Answer (in meters):
Transcribed Image Text:A car is moving with speed 35 m/s and acceleration 3 m/s² at the given instant. Using a second-degree Taylor polynomial, estimate how far the car moves in the next second. Answer (in meters):
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