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).

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.4: Plane Curves And Parametric Equations
Problem 20E
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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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