For Exercises 71-72, use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where x , y , and z are rounded to 2 decimal places. − 3.61 x + 8.17 y − 5.62 z = 30.2 8.04 x − 3.16 y + 9.18 z = 28.4 − 0.16 + 0.09 y + 0.55 z = 4.6
For Exercises 71-72, use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where x , y , and z are rounded to 2 decimal places. − 3.61 x + 8.17 y − 5.62 z = 30.2 8.04 x − 3.16 y + 9.18 z = 28.4 − 0.16 + 0.09 y + 0.55 z = 4.6
Solution Summary: The author explains how to calculate the reduced row-echelon form of a linear system using calculator.
For Exercises 71-72, use a calculator to approximate the reduced row-echelon form of the augmented matrix representing the given system. Give the solution set where
x
,
y
, and
z
are rounded to
2
decimal places.
−
3.61
x
+
8.17
y
−
5.62
z
=
30.2
8.04
x
−
3.16
y
+
9.18
z
=
28.4
−
0.16
+
0.09
y
+
0.55
z
=
4.6
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
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