Graphical, Numerical, and Analytic Analysis In Exercises 75-82, use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. lim x → 0 [ 1 / ( 2 + x ) ] − ( 1 / 2 ) x
Graphical, Numerical, and Analytic Analysis In Exercises 75-82, use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods. lim x → 0 [ 1 / ( 2 + x ) ] − ( 1 / 2 ) x
Solution Summary: The author explains how to calculate the transcendental function's limit by graphing.
Graphical, Numerical, and Analytic Analysis In Exercises 75-82, use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods.
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 1 Solutions
Student Solutions Manual for Larson/Edwards' Calculus of a Single Variable, 11th
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