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(a) x= 3t — 4, y = 6t + 2 (b) x=2cos(t), y=5sin(t) (0 ≤t≤ 2π) (c) x= 2sin²(t), y = 3cos²(t) (0

(a) x= 3t — 4, y = 6t + 2 (b) x=2cos(t), y=5sin(t) (0 ≤t≤ 2π) (c) x= 2sin²(t), y = 3cos²(t) (0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transcription for Educational Website** --- **Parameter Elimination and Curve Sketching** *Objective:* Sketch the curve by eliminating the parameter, and indicate the direction of increasing \( t \). **Problems:** (a) \[ x = 3t - 4, \quad y = 6t + 2 \] (b) \[ x = 2\cos(t), \quad y = 5\sin(t) \quad (0 \leq t \leq 2\pi) \] (c) \[ x = 2\sin^2(t), \quad y = 3\cos^2(t) \quad \left(0 \leq t \leq \frac{\pi}{2}\right) \] --- *Instructions:* 1. Find a relationship between \( x \) and \( y \) by eliminating \( t \). 2. Sketch the resulting curve in the \( xy \)-plane. 3. Indicate the direction in which the curve is traced as \( t \) increases. ---
Transcribed Image Text:**Transcription for Educational Website** --- **Parameter Elimination and Curve Sketching** *Objective:* Sketch the curve by eliminating the parameter, and indicate the direction of increasing \( t \). **Problems:** (a) \[ x = 3t - 4, \quad y = 6t + 2 \] (b) \[ x = 2\cos(t), \quad y = 5\sin(t) \quad (0 \leq t \leq 2\pi) \] (c) \[ x = 2\sin^2(t), \quad y = 3\cos^2(t) \quad \left(0 \leq t \leq \frac{\pi}{2}\right) \] --- *Instructions:* 1. Find a relationship between \( x \) and \( y \) by eliminating \( t \). 2. Sketch the resulting curve in the \( xy \)-plane. 3. Indicate the direction in which the curve is traced as \( t \) increases. ---
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