Differentiate the functions in Exercises 11 − 20 using one or more of the differentiation rules discussed thus far. Given f ( 1 ) = 1 , f ' ( 1 ) = 5 , g ( 1 ) = 3 , g ' ( 1 ) = 4 , f ' ( 3 ) = 2 and g ' ( 3 ) = 6 , compute the following derivatives: d d x [ g ( f ( x ) ) ] | x = 1
Differentiate the functions in Exercises 11 − 20 using one or more of the differentiation rules discussed thus far. Given f ( 1 ) = 1 , f ' ( 1 ) = 5 , g ( 1 ) = 3 , g ' ( 1 ) = 4 , f ' ( 3 ) = 2 and g ' ( 3 ) = 6 , compute the following derivatives: d d x [ g ( f ( x ) ) ] | x = 1
Solution Summary: The author explains how to calculate dg(f(x))|_x=1=20.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Chapter 3 Solutions
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