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I. Let C be the curve with parametric equations I = 3t-1² t and yIn(t-1) for t = (1, +∞), and let P be the point (0, In 2). 1. Find the value of t which corresponds to the point P. 2. Without finding a Cartesian equation for the curve C, find an equation of the tangent line to Cat the point P. Leave your answer in point-slope form. 3. Determine if C is concave up or down at P.

I. Let C be the curve with parametric equations I = 3t-1² t and yIn(t-1) for t = (1, +∞), and let P be the point (0, In 2). 1. Find the value of t which corresponds to the point P. 2. Without finding a Cartesian equation for the curve C, find an equation of the tangent line to Cat the point P. Leave your answer in point-slope form. 3. Determine if C is concave up or down at P.

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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I. Let C be the curve with parametric equations I = 3t-1² t-1 and yIn(t-1) for t€ (1, +∞0), and let P be the point (0, In 2). 1. Find the value of t which corresponds to the point P. 2. Without finding a Cartesian equation for the curve C, find an equation of the tangent line to Cat the point P. Leave your answer in point-slope form. 3. Determine if C is concave up or down at P.
Transcribed Image Text:I. Let C be the curve with parametric equations I = 3t-1² t-1 and yIn(t-1) for t€ (1, +∞0), and let P be the point (0, In 2). 1. Find the value of t which corresponds to the point P. 2. Without finding a Cartesian equation for the curve C, find an equation of the tangent line to Cat the point P. Leave your answer in point-slope form. 3. Determine if C is concave up or down at P.
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