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1. Two-part question: a. Graph the parametric equation. x = −t, y = f² +1+1; only on the interval −1 < t <2₂ putting arrows on the graph to indicate the orientation. b. Find an equation of the tangent line to the curve at the point (0, 3).

1. Two-part question: a. Graph the parametric equation. x = −t, y = f² +1+1; only on the interval −1 < t <2₂ putting arrows on the graph to indicate the orientation. b. Find an equation of the tangent line to the curve at the point (0, 3).

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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Can you please answer the following questions.

1. Two-part question: a. Graph the parametric equation. x = −t; y = ? +t+1; only on the interval −1 < t <2, putting arrows on the graph to indicate the orientation. b. Find an equation of the tangent line to the curve at the point (0, 3). 2. Two-part question: a. Identify the curve given by r = -3sec by finding a Cartesian equation for it. 8 b. Find the slope of the tangent line to the polar curve >= cos at the point where 8 = π. 3. Two-part question: a. Find the Taylor series for f(x) = e centered at the value a = 5. (Assume that f(x) has a power series expansion. Do not show that R₂(x) →0.) Use a chart to show the values of n, f(n)(x), and f(n)(a) = f(") (5). That is, find: f(x)=Σ(?) -Ė (?) 22-0 R = ? b. Find the associated radius of convergence R.
Transcribed Image Text:1. Two-part question: a. Graph the parametric equation. x = −t; y = ? +t+1; only on the interval −1 < t <2, putting arrows on the graph to indicate the orientation. b. Find an equation of the tangent line to the curve at the point (0, 3). 2. Two-part question: a. Identify the curve given by r = -3sec by finding a Cartesian equation for it. 8 b. Find the slope of the tangent line to the polar curve >= cos at the point where 8 = π. 3. Two-part question: a. Find the Taylor series for f(x) = e centered at the value a = 5. (Assume that f(x) has a power series expansion. Do not show that R₂(x) →0.) Use a chart to show the values of n, f(n)(x), and f(n)(a) = f(") (5). That is, find: f(x)=Σ(?) -Ė (?) 22-0 R = ? b. Find the associated radius of convergence R.
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