For Exercises 5-8 a. Evaluate the determinant of the coefficient matrix. b. Based on the value of the determinant from part (a), can an inverse matrix or Cramer's rule be used to solve the system? c. Solve the system using an appropriate method. x − 2 y + 3 z = − 7 − 2 x + y = − 1 x − z = 3
For Exercises 5-8 a. Evaluate the determinant of the coefficient matrix. b. Based on the value of the determinant from part (a), can an inverse matrix or Cramer's rule be used to solve the system? c. Solve the system using an appropriate method. x − 2 y + 3 z = − 7 − 2 x + y = − 1 x − z = 3
Solution Summary: The determinant of the coefficient matrix for the given system of equations is 0.
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).
College Algebra with Modeling & Visualization (5th Edition)
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HOW TO FIND DETERMINANT OF 2X2 & 3X3 MATRICES?/MATRICES AND DETERMINANTS CLASS XII 12 CBSE; Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=bnaKGsLYJvQ;License: Standard YouTube License, CC-BY