Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Question
Chapter 3, Problem 1PE
(a)
To determine
The meaning of slope of the tangent line.
(a)
Expert Solution
Explanation of Solution
A tangent to a function
Tangent line is parallel to graph of function given in the problem.
So,
Slope of tangent line tells us the rate of change at a particular instant.
(b)
To determine
The comparison of slope of the tangent line to the slope of the secant line.
(b)
Expert Solution
Explanation of Solution
Secant line is the line that touches the graph at a single point, that is not parallel to the graph of the function whereas tangent line is the line that touches the graph at a single point, that is parallel to graph of the function.
(c)
To determine
The meaning of normal line to a graph.
(c)
Expert Solution
Explanation of Solution
Normal line is the line that is perpendicular to the tangent line to the graph of function given in the problem.
The slope of the normal line is the negative reciprocal of the slope of the tangent line.
A normal line can touch the graph of the function at more than one point.
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Students have asked these similar questions
3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
Chapter 3 Solutions
Student's Solution and Survival Manual for Calculus
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