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7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te²4), g(t) = (-e2", 1– t), for t E R. In(t) for t > 0. 2 Also consider the function s: (0, 00) R given by s(t) (a) Find (fo s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.

7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te²4), g(t) = (-e2", 1– t), for t E R. In(t) for t > 0. 2 Also consider the function s: (0, 00) R given by s(t) (a) Find (fo s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
Problem 30EQ
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7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te2t), g(t) = (-e2“, 1 – t²), for t E R. In(t) Also consider the function s: (0, 0) → R given by s(t) for t > 0. 2 (a) Find (f o s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.
Transcribed Image Text:7. Consider the functions f, g: R → R² given by: f(t) = (t(2t – 3), te2t), g(t) = (-e2“, 1 – t²), for t E R. In(t) Also consider the function s: (0, 0) → R given by s(t) for t > 0. 2 (a) Find (f o s)'(t), for t > 0. (b) Find (f g)'(t), for t e R.
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