Finite Mathematics and Calculus with Applications
1st Edition
ISBN: 9781323188361
Author: Margaret Lial
Publisher: Pearson Education
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Chapter R.6, Problem 7E
To determine
To evaluate: The expression
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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 R Solutions
Finite Mathematics and Calculus with Applications
Ch. R.1 - Perform the operation 3(x24x5)4(3x25x7)Ch. R.1 - Perform the operation (3y+2)(4y22y5).Ch. R.1 - Find (2x+7)(3x1) using the FOIL method.Ch. R.1 - Find (3x+2y)3.Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....
Ch. R.1 - Perform the indicated operations. 7.9m(2m2+3m1)Ch. R.1 - Perform the indicated operations. 86x(2x3+5x+6)Ch. R.1 - Prob. 9ECh. R.1 - Perform the indicated operations. 10.(9k+q)(2kq)Ch. R.1 - Perform the indicated operations. 11.(23x)(2+3x)Ch. R.1 - Perform the indicated operations. 12.(6m+5)(6m5)Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations....Ch. R.1 - Perform the indicated operations. 22.(x1)(x+2)(x3)Ch. R.1 - Perform the indicated operations. 23.(x+2)2Ch. R.1 - Perform the indicated operations. 24.(2a4b)2Ch. R.1 - Perform the indicated operations. 25.(x2y)3Ch. R.1 - Perform the indicated operations. 26.(3y+y)3Ch. R.2 - Factor 4z4+4z3+18z2.Ch. R.2 - Factor x23x10.Ch. R.2 - Factor 6a2+5ab4b2.Ch. R.2 - Factor each polynomial. If a polynomial cannot he...Ch. R.2 - Prob. 2ECh. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Prob. 6ECh. R.2 - Prob. 7ECh. R.2 - Prob. 8ECh. R.2 - Prob. 9ECh. R.2 - Prob. 10ECh. R.2 - Prob. 11ECh. R.2 - Prob. 12ECh. R.2 - Prob. 13ECh. R.2 - Prob. 14ECh. R.2 - Prob. 15ECh. R.2 - Prob. 16ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 18ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 20ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 22ECh. R.2 - Prob. 23ECh. R.2 - Prob. 24ECh. R.2 - Prob. 25ECh. R.2 - Prob. 26ECh. R.2 - Prob. 27ECh. R.2 - Prob. 28ECh. R.2 - Factor each polynomial. If a polynomial cannot be...Ch. R.2 - Prob. 30ECh. R.2 - Prob. 31ECh. R.2 - Prob. 32ECh. R.3 - Write in lowest terms z2+5z+62z2+7z+3.Ch. R.3 - Prob. 2YTCh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 2ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 4ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 6ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 8ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 10ECh. R.3 - Write each rational expression in lowest terms....Ch. R.3 - Prob. 12ECh. R.3 - Prob. 13ECh. R.3 - Prob. 14ECh. R.3 - Prob. 15ECh. R.3 - Perform the indicated operations. 16.a316a332Ch. R.3 - Perform the indicated operations. 17.2k1664k323Ch. R.3 - Prob. 18ECh. R.3 - Prob. 19ECh. R.3 - Perform the indicated operations....Ch. R.3 - Prob. 21ECh. R.3 - Prob. 22ECh. R.3 - Prob. 23ECh. R.3 - Prob. 24ECh. R.3 - Prob. 25ECh. R.3 - Prob. 26ECh. R.3 - Prob. 27ECh. R.3 - Perform the indicated operations. 28.16m+25m+4mCh. R.3 - Prob. 29ECh. R.3 - Prob. 30ECh. R.3 - Prob. 31ECh. R.3 - Prob. 32ECh. R.3 - Prob. 33ECh. R.3 - Prob. 34ECh. R.3 - Prob. 35ECh. R.3 - Prob. 36ECh. R.3 - Prob. 37ECh. R.3 - Prob. 38ECh. R.4 - Solve 3x7=4(5x+2)7x.Ch. R.4 - Solve 2m2+7m=15.Ch. R.4 - Solve z2+6=8z.Ch. R.4 - Solve 1x24+2x2=1x.Ch. R.4 - Prob. 1ECh. R.4 - Prob. 2ECh. R.4 - Solve each equation. 3.0.2m0.5=0.1m+0.7Ch. R.4 - Prob. 4ECh. R.4 - Solve each equation. 5.3r+25(r+1)=6r+4Ch. R.4 - Solve each equation. 6.5(a+3)+4a5=(2a4)Ch. R.4 - Solve each equation. 7.2[3m2(3m)4]=6m4Ch. R.4 - Solve each equation. 8.4[2p(3p)+5]=7p2Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 10ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 21ECh. R.4 - Prob. 22ECh. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Solve each equation by factoring or by using the...Ch. R.4 - Prob. 27ECh. R.4 - Prob. 28ECh. R.4 - Solve each equation. 29.4x382x+5+3x3=0Ch. R.4 - Solve each equation. 30.5p27p+2=12p24Ch. R.4 - Solve each equation. 31.2mm26m=12m22mCh. R.4 - Solve each equation. 32.2yy1=5y+108yy2yCh. R.4 - Solve each equation. 33.1x23xx1=2x+1x23x+2Ch. R.4 - Solve each equation. 34.5a+7a+1=a22a+4a2+aCh. R.4 - Solve each equation. 35.5b+54b2+2b=6b2+7b+10Ch. R.4 - Solve each equation. 36.2x22x3+5x2x6=1x2+3x+2Ch. R.4 - Prob. 37ECh. R.5 - Prob. 1YTCh. R.5 - Prob. 2YTCh. R.5 - Prob. 3YTCh. R.5 - Prob. 1ECh. R.5 - Prob. 2ECh. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Write each expression in interval notation, Graph...Ch. R.5 - Prob. 5ECh. R.5 - Prob. 6ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 8ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 10ECh. R.5 - Prob. 11ECh. R.5 - Prob. 12ECh. R.5 - Using the variable x, write each interval as an...Ch. R.5 - Prob. 14ECh. R.5 - Prob. 15ECh. R.5 - Prob. 16ECh. R.5 - Prob. 17ECh. R.5 - Prob. 18ECh. R.5 - Solve each inequality and graph the solution....Ch. R.5 - Prob. 20ECh. R.5 - Prob. 21ECh. R.5 - Prob. 22ECh. R.5 - Solve each inequality and graph the solution....Ch. R.5 - Prob. 24ECh. R.5 - Prob. 25ECh. R.5 - Prob. 26ECh. R.5 - Prob. 27ECh. R.5 - Prob. 28ECh. R.5 - Prob. 29ECh. R.5 - Prob. 30ECh. R.5 - Solve each inequality. Graph each solution....Ch. R.5 - Prob. 32ECh. R.5 - Prob. 33ECh. R.5 - Prob. 34ECh. R.5 - Prob. 35ECh. R.5 - Prob. 36ECh. R.5 - Prob. 37ECh. R.5 - Prob. 38ECh. R.5 - Prob. 39ECh. R.5 - Prob. 40ECh. R.5 - Prob. 41ECh. R.5 - Prob. 42ECh. R.5 - Prob. 43ECh. R.5 - Prob. 44ECh. R.5 - Solve each inequality. 45.k1k+21Ch. R.5 - Prob. 46ECh. R.5 - Prob. 47ECh. R.5 - Prob. 48ECh. R.5 - Prob. 49ECh. R.5 - Prob. 50ECh. R.5 - Prob. 51ECh. R.5 - Prob. 52ECh. R.5 - Prob. 53ECh. R.5 - Prob. 54ECh. R.6 - Prob. 1YTCh. R.6 - Prob. 2YTCh. R.6 - Prob. 3YTCh. R.6 - Prob. 4YTCh. R.6 - Prob. 5YTCh. R.6 - Prob. 6YTCh. R.6 - Prob. 1ECh. R.6 - Prob. 2ECh. R.6 - Prob. 3ECh. R.6 - Prob. 4ECh. R.6 - Prob. 5ECh. R.6 - Prob. 6ECh. R.6 - Prob. 7ECh. R.6 - Prob. 8ECh. R.6 - Prob. 9ECh. R.6 - Prob. 10ECh. R.6 - Prob. 11ECh. R.6 - Prob. 12ECh. R.6 - Prob. 13ECh. R.6 - Prob. 14ECh. R.6 - Prob. 15ECh. R.6 - Prob. 16ECh. R.6 - Prob. 17ECh. R.6 - Prob. 18ECh. R.6 - Prob. 19ECh. R.6 - Prob. 20ECh. R.6 - Prob. 21ECh. R.6 - Prob. 22ECh. R.6 - Prob. 23ECh. R.6 - Prob. 24ECh. R.6 - Prob. 25ECh. R.6 - Prob. 26ECh. R.6 - Write each number without exponents. 27.1211/2Ch. R.6 - Prob. 28ECh. R.6 - Prob. 29ECh. R.6 - Prob. 30ECh. R.6 - Prob. 31ECh. R.6 - Prob. 32ECh. R.6 - Prob. 33ECh. R.6 - Prob. 34ECh. R.6 - Prob. 35ECh. R.6 - Prob. 36ECh. R.6 - Prob. 37ECh. R.6 - Prob. 38ECh. R.6 - Prob. 39ECh. R.6 - Prob. 40ECh. R.6 - Prob. 41ECh. R.6 - Prob. 42ECh. R.6 - Prob. 43ECh. R.6 - Prob. 44ECh. R.6 - Prob. 45ECh. R.6 - Prob. 46ECh. R.6 - Prob. 47ECh. R.6 - Simplify each expression. Write all answers with...Ch. R.6 - Prob. 49ECh. R.6 - Prob. 50ECh. R.6 - Prob. 51ECh. R.6 - Prob. 52ECh. R.6 - Prob. 53ECh. R.6 - Prob. 54ECh. R.6 - Prob. 55ECh. R.6 - Prob. 56ECh. R.7 - Simplify 28x9y5.Ch. R.7 - Rationalize the denominator in 5xy.Ch. R.7 - Rationalize the numerator in 4+x16x.Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 4ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 7ECh. R.7 - Prob. 8ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 16ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 18ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 20ECh. R.7 - Simplify each expression by removing as many...Ch. R.7 - Prob. 22ECh. R.7 - Prob. 23ECh. R.7 - Prob. 24ECh. R.7 - Prob. 25ECh. R.7 - Simplify each root, if possible. 26.9k2+h2Ch. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 28ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 30ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 32ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 34ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 36ECh. R.7 - Prob. 37ECh. R.7 - Prob. 38ECh. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Rationalize each denominator. Assume that all...Ch. R.7 - Prob. 42ECh. R.7 - Prob. 43ECh. R.7 - Rationalize each denominator. Assume that all...
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- Question 2 Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let (P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is -2.024 1.391 0.186 -0.994 -2.053 -0.647 -0.588 -1.851 1 ptsarrow_forward1 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 .arrow_forwardanswerarrow_forward
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