83. Second Derivative for a Parametrized Curve Given a parametrized curve c(t) = (x(t), y(t)), show that x'(t)y" (t) – y'(t)x"(1) x'(t)? d (dy dt dx Use this to prove the formula x'(t) y"(t)- y'(t)x" (t) d²y dx2 13 x'(t)3

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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83. Second Derivative for a Parametrized Curve Given a parametrized curve c(t) = (x(t), y(t)), show
that
x'(t)y" (t) – y'(t)x"(1)
x'(t)?
d (dy
dt dx
Use this to prove the formula
x'(t) y"(t)- y'(t)x" (t)
d²y
dx2
13
x'(t)3
Transcribed Image Text:83. Second Derivative for a Parametrized Curve Given a parametrized curve c(t) = (x(t), y(t)), show that x'(t)y" (t) – y'(t)x"(1) x'(t)? d (dy dt dx Use this to prove the formula x'(t) y"(t)- y'(t)x" (t) d²y dx2 13 x'(t)3
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