EBK CALCULUS:EARLY TRANSCENDENTALS
11th Edition
ISBN: 9781119244912
Author: Anton
Publisher: WILEY CONS
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Chapter 12.1, Problem 2ES
Find the domain of
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8–23. Sketching vector fields Sketch the following vector fields
25-30. Normal and tangential components For the vector field F and
curve C, complete the following:
a. Determine the points (if any) along the curve C at which the vector
field F is tangent to C.
b. Determine the points (if any) along the curve C at which the vector
field F is normal to C.
c. Sketch C and a few representative vectors of F on C.
25. F
=
(2½³, 0); c = {(x, y); y −
x² =
1}
26. F
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x
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,
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27. F(x, y); C = {(x, y): x² + y² = 4}
28. F = (y, x); C = {(x, y): x² + y² = 1}
29. F = (x, y); C =
30. F = (y, x); C =
{(x, y): x = 1}
{(x, y): x² + y² = 1}
Chapter 12 Solutions
EBK CALCULUS:EARLY TRANSCENDENTALS
Ch. 12.1 - Prob. 1QCECh. 12.1 - Describe the graph of rt=1+2t,1+3t.Ch. 12.1 - Prob. 3QCECh. 12.1 - Prob. 4QCECh. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Find the domain of rt and the value of rt0....Ch. 12.1 - Prob. 5ESCh. 12.1 - Prob. 6ES
Ch. 12.1 - Prob. 7ESCh. 12.1 - Prob. 8ESCh. 12.1 - Describe the graph of the equation. r=32ti+5tjCh. 12.1 - Describe the graph of the equation....Ch. 12.1 - Describe the graph of the equation. r=2ti3j+1+3tkCh. 12.1 - Prob. 12ESCh. 12.1 - Describe the graph of the equation....Ch. 12.1 - Describe the graph of the equation. r=3i+1t2j+tkCh. 12.1 - (a) Find the slope of the line in 2-space that is...Ch. 12.1 - (a) Find the y-intercept of the line in 2-space...Ch. 12.1 - Prob. 17ESCh. 12.1 - Sketch the line segment represented by each vector...Ch. 12.1 - Write a vector equation for the line segment from...Ch. 12.1 - Write a vector equation for the line segment from...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Sketch the graph of rt and show the direction of...Ch. 12.1 - Prob. 31ESCh. 12.1 - Prob. 32ESCh. 12.1 - Determine whether the statement is true or false....Ch. 12.1 - Determine whether the statement is true or false....Ch. 12.1 - Sketch the curve of intersection of the surfaces,...Ch. 12.1 - Sketch the curve of intersection of the surfaces,...Ch. 12.1 - Sketch the curve of intersection of the surfaces,...Ch. 12.1 - Prob. 38ESCh. 12.1 - Show that the graph of r=tsinti+tcostj+t2k lies on...Ch. 12.1 - Show that the graph of r=ti+1+ttj+1t2tk,t0 lies in...Ch. 12.1 - Prob. 41ESCh. 12.1 - Show that the graph of r=3costi+3sintj+3sintk is...Ch. 12.1 - Prob. 43ESCh. 12.1 - How many revolutions will the circular helix...Ch. 12.1 - Show that the curve r=tcosti+tsintj+tk,t0, lies on...Ch. 12.1 - Describe the curve r=acosti+bsintj+ctk, where...Ch. 12.1 - In each part, match the vector equation with one...Ch. 12.1 - (a) Find parametric equations for the curve of...Ch. 12.1 - (a) Sketch the graph of rt=2t,21+t2 (b) Prove that...Ch. 12.1 - Prob. 51ESCh. 12.1 - Suppose that r1tandr2t are vector-valued functions...Ch. 12.2 - alimt3t2i+2tj=blimt/4cost,sint=Ch. 12.2 - Find r t. art=4+5ti+tt2jbrt=1t,tant,e2tCh. 12.2 - Suppose that r10=3,2,1,r20=1,2,3,r 10=0,0,0,andr...Ch. 12.2 - a012t,t2,sintdt=bti3t2j+etkdt=Ch. 12.2 - Find the limit. limt+t2+13t2+2,1tCh. 12.2 - Prob. 2ESCh. 12.2 - Find the limit. limt2ti3j+t2kCh. 12.2 - Prob. 4ESCh. 12.2 - Determine whether rt is continuous at t=0. Explain...Ch. 12.2 - Determine whether rt is continuous at t=0. Explain...Ch. 12.2 - Sketch the circle rt=costi+sintj, draw the vector...Ch. 12.2 - Sketch the circle rt=costi+sintj, draw the vector...Ch. 12.2 - Find r t. rt=4icostjCh. 12.2 - Find r t. rt=tan1ti+tcostjtkCh. 12.2 - Prob. 11ESCh. 12.2 - Prob. 12ESCh. 12.2 - Prob. 13ESCh. 12.2 - Find the vector rt0; then sketch the graph of rt...Ch. 12.2 - Find the vector rt0; then sketch the graph of rt...Ch. 12.2 - Prob. 16ESCh. 12.2 - Use a graphing utility to generate the graph of rt...Ch. 12.2 - Use a graphing utility to generate the graph of rt...Ch. 12.2 - Find parametric equations of the line tangent to...Ch. 12.2 - Find parametric equations of the line tangent to...Ch. 12.2 - Find parametric equations of the line tangent to...Ch. 12.2 - Find parametric equations of the line tangent to...Ch. 12.2 - Prob. 23ESCh. 12.2 - Find a vector equation of the line tangent to the...Ch. 12.2 - Prob. 25ESCh. 12.2 - Prob. 26ESCh. 12.2 - Letrt=costi+sintj+k.findalimt0rtr tblimt0rtr...Ch. 12.2 - Prob. 28ESCh. 12.2 - Calculate ddtr1tr2tandddtr1tr2t first by...Ch. 12.2 - Calculate ddtr1tr2tandddtr1tr2t first by...Ch. 12.2 - Evaluate the indefinite integral. 3i+4tjdtCh. 12.2 - Evaluate the indefinite integral. t2i2tj+1tkdtCh. 12.2 - Evaluate the indefinite integral. tet,lntdtCh. 12.2 - Evaluate the indefinite integral. et,et,3t2dtCh. 12.2 - Evaluate the definite integral. 0/2cos2t,sin2tdtCh. 12.2 - Evaluate the definite integral. 01t2i+t3jdtCh. 12.2 - Evaluate the definite integral. 02ti+t2jdtCh. 12.2 - Evaluate the definite integral. 333t3/2,3+t3/2,1dtCh. 12.2 - Evaluate the definite integral. 19t1/2i+t1/2jdtCh. 12.2 - Evaluate the definite integral. 01e2ti+etj+tkdtCh. 12.2 - Prob. 41ESCh. 12.2 - Determine whether the statement is true or false....Ch. 12.2 - Prob. 43ESCh. 12.2 - Prob. 44ESCh. 12.2 - Solve the vector initial-value problem for yt by...Ch. 12.2 - Solve the vector initial-value problem for yt by...Ch. 12.2 - Solve the vector initial-value problem for yt by...Ch. 12.2 - Solve the vector initial-value problem for yt by...Ch. 12.2 - (a) Find the points where the curve r=ti+t2j3tk...Ch. 12.2 - Find where the tangent line to the curve...Ch. 12.2 - Show that the graphs of r1tandr2t intersect at the...Ch. 12.2 - Show that the graphs of r1tandr2t intersect at the...Ch. 12.2 - Use Formula (7) to derive the differentiation...Ch. 12.2 - Let u=ut,v=vt,andw=wt be differentiable...Ch. 12.2 - Let u1,u2,u3,1,2,3,w1,w2,andw3, be differentiable...Ch. 12.2 - Prove Theorem 12.2.6 for 2-space.Ch. 12.2 - Derive Formulas (6) and (7) for 3-space.Ch. 12.2 - Prove Theorem 12.2.9 for 2-space.Ch. 12.2 - Prob. 59ESCh. 12.2 - Prob. 60ESCh. 12.3 - If rt is a smooth vector-valued function, then the...Ch. 12.3 - If r(s) is a smooth vector-valued function...Ch. 12.3 - If rt is a smooth vector-valued function, then the...Ch. 12.3 - Suppose that rt is a smooth vector-valued function...Ch. 12.3 - Determine whether rt is a smooth function of the...Ch. 12.3 - Determine whether rt is a smooth function of the...Ch. 12.3 - Determine whether rt is a smooth function of the...Ch. 12.3 - Determine whether rt is a smooth function of the...Ch. 12.3 - Find the arc length of the parametric curve....Ch. 12.3 - Find the arc length of the parametric curve....Ch. 12.3 - Find the arc length of the parametric curve....Ch. 12.3 - Find the arc length of the parametric curve....Ch. 12.3 - Find the arc length of the graph of rt....Ch. 12.3 - Find the arc length of the graph of rt....Ch. 12.3 - Find the arc length of the graph of rt....Ch. 12.3 - Find the arc length of the graph of rt....Ch. 12.3 - Calculate dr/d by the chain rule, and then check...Ch. 12.3 - Calculate dr/d by the chain rule, and then check...Ch. 12.3 - Calculate dr/d by the chain rule, and then check...Ch. 12.3 - Calculate dr/d by the chain rule, and then check...Ch. 12.3 - Prob. 17ESCh. 12.3 - Prob. 18ESCh. 12.3 - Prob. 19ESCh. 12.3 - Prob. 20ESCh. 12.3 - (a) Find the arc length parametrization of the...Ch. 12.3 - Find arc length parametrizations of the lines in...Ch. 12.3 - Prob. 23ESCh. 12.3 - (a) Find the arc length parametrization of the...Ch. 12.3 - Find an arc length parametrization of the curve...Ch. 12.3 - Find an arc length parametrization of the curve...Ch. 12.3 - Find an arc length parametrization of the curve...Ch. 12.3 - Find an arc length parametrization of the curve...Ch. 12.3 - Find an arc length parametrization of the curve...Ch. 12.3 - Find an arc length parametrization of the curve...Ch. 12.3 - Show that the arc length of the circular helix...Ch. 12.3 - Use the result in Exercise 31 to show the circular...Ch. 12.3 - Find an arc length parametrization of the cycloid...Ch. 12.3 - Show that in cylindrical coordinates a curve given...Ch. 12.3 - In each part, use the formula in Exercise 34 to...Ch. 12.3 - Show That in spherical coordinates a curve given...Ch. 12.3 - In each part, use the formula in Exercise 36 to...Ch. 12.3 - h (a) Sketch the graph of rt=ti+t2j. Show that rt...Ch. 12.3 - Find a change of parameter t=g for the semicircle...Ch. 12.3 - What change of parameter t=g would you make if you...Ch. 12.3 - As illustrated in the accompanying figure, copper...Ch. 12.3 - Let rt=cost,sint,t3/2.Findartbdsdtc02rtdt.Ch. 12.3 - Let rt=lnti+2tj+t2k.Findartbdsdtc13rtdt.Ch. 12.3 - Let rt=t2i+t3j (seeFigure12.3.1) . Let t be the...Ch. 12.3 - Prove: If rt is a smoothly parametrized function,...Ch. 12.3 - Prove the vector form of the chain rule for...Ch. 12.3 - Prob. 47ESCh. 12.4 - Prob. 1QCECh. 12.4 - If C is the graph of a smooth vector-valued...Ch. 12.4 - If C is the graph of a smooth vector-valued...Ch. 12.4 - Suppose that C is the graph of a smooth...Ch. 12.4 - In each part, sketch the unit tangent and normal...Ch. 12.4 - Make a rough sketch that shows the ellipse...Ch. 12.4 - In the marginal note associated with Example 8 of...Ch. 12.4 - Use the result in Exercise 3 to show that the...Ch. 12.4 - Find TtandNt at the given point. rt=t21i+tj;t=1Ch. 12.4 - Find TtandNt at the given point....Ch. 12.4 - Find TtandNt at the given point....Ch. 12.4 - Find TtandNt at the given point. rt=lnti+tj;t=eCh. 12.4 - Find TtandNt at the given point....Ch. 12.4 - Find TtandNt at the given point....Ch. 12.4 - Find TtandNt at the given point....Ch. 12.4 - Find TtandNt at the given point....Ch. 12.4 - Use the result in Exercise 3 to find parametric...Ch. 12.4 - Use the result in Exercise 3 to find parametric...Ch. 12.4 - Use the formula Bt=TtNt to find Bt, and then check...Ch. 12.4 - Use the formula Bt=TtNt to find Bt, and then check...Ch. 12.4 - Use the formula Bt=TtNt to find Bt, and then check...Ch. 12.4 - Prob. 18ESCh. 12.4 - Find Tt,Nt,andBt for the given value of t. Then...Ch. 12.4 - Find Tt,Nt,andBt for the given value of t. Then...Ch. 12.4 - Prob. 21ESCh. 12.4 - Prob. 22ESCh. 12.4 - Determine whether the statement is true or false....Ch. 12.4 - Prob. 24ESCh. 12.4 - Discuss some of the advantages of parametrizing a...Ch. 12.5 - If C is a smooth curve parametrized by arc length,...Ch. 12.5 - Let rt be a smooth vector-valued function with...Ch. 12.5 - Suppose that C is the graph of a smooth...Ch. 12.5 - Suppose that C is a smooth curve and that x2+y2=4...Ch. 12.5 - Use the osculating circle shown in the figure to...Ch. 12.5 - Use the osculating circle shown in the figure to...Ch. 12.5 - For a plane curve y=fx the curvature at x,fx is...Ch. 12.5 - For a plane curve y=fx the curvature at x,fx is...Ch. 12.5 - Use Formula (3) to find t. rt=t2i+t3jCh. 12.5 - Use Formula (3) to find t. rt=4costi+sintjCh. 12.5 - Use Formula (3) to find t. rt=e3ti+etjCh. 12.5 - Use Formula (3) to find t. x=1t3,y=tt2Ch. 12.5 - Use Formula (3) to find t. rt=4costi+4sintj+tkCh. 12.5 - Prob. 10ESCh. 12.5 - Use Formula (3) to find t. x=cosht,y=sinht,z=tCh. 12.5 - Use Formula (3) to find t. rt=i+tj+t3kCh. 12.5 - Find the curvature and the radius of curvature at...Ch. 12.5 - Find the curvature and the radius of curvature at...Ch. 12.5 - Find the curvature and the radius of curvature at...Ch. 12.5 - Find the curvature and the radius of curvature at...Ch. 12.5 - Confirm that s is an arc length parameter by...Ch. 12.5 - Confirm that s is an arc length parameter by...Ch. 12.5 - Determine whether the statement is true or false....Ch. 12.5 - Determine whether the statement is true or false....Ch. 12.5 - Determine whether the statement is true or false....Ch. 12.5 - Determine whether the statement is true or false....Ch. 12.5 - (a) Use Formula (3) to show that in 2-space the...Ch. 12.5 - Use part (b) of Exercise 23 to show that the...Ch. 12.5 - Use the result in Exercise 23(b) to find the...Ch. 12.5 - Use the result in Exercise 23(b) to find the...Ch. 12.5 - Use the result in Exercise 23(b) to find the...Ch. 12.5 - Use the result in Exercise 23(b) to find the...Ch. 12.5 - Use the result in Exercise 23(a) to find the...Ch. 12.5 - Use the result in Exercise 23(a) to find the...Ch. 12.5 - Use the result in Exercise 23(a) to find the...Ch. 12.5 - Use the result in Exercise 23(a) to find the...Ch. 12.5 - In each part, use the formulas in Exercise 23 to...Ch. 12.5 - Prob. 34ESCh. 12.5 - Generate the graph of y=fx using a graphing...Ch. 12.5 - Generate the graph of y=fx using a graphing...Ch. 12.5 - Prob. 37ESCh. 12.5 - (a) Use a CAS to graph the parametric curve...Ch. 12.5 - Use the formula in Exercise 23 (a) to show that...Ch. 12.5 - Use the result in Exercise 39 to show that a...Ch. 12.5 - Use the formula in Exercise 39 to find the...Ch. 12.5 - Use the formula in Exercise 39 to find the...Ch. 12.5 - Use the formula in Exercise 39 to find the...Ch. 12.5 - Use the formula in Exercise 39 to find the...Ch. 12.5 - Find the radius of curvature of the parabola...Ch. 12.5 - At what point(s) does y=ex have maximum curvature...Ch. 12.5 - At what point(s) does 4x2+9y2=36 have a minimum...Ch. 12.5 - Find the maximum and minimum values of the radius...Ch. 12.5 - Use the formula in Exercise 39 to show that the...Ch. 12.5 - Use the formula in Exercise 39 and a CAS to show...Ch. 12.5 - Prob. 51ESCh. 12.5 - The evolute of a smooth parametric curve C in...Ch. 12.5 - These exercises are concerned with the problem of...Ch. 12.5 - These exercises are concerned with the problem of...Ch. 12.5 - These exercises are concerned with the problem of...Ch. 12.5 - These exercises are concerned with the problem of...Ch. 12.5 - These exercises are concerned with the problem of...Ch. 12.5 - Assume that s is an arc length parameter for a...Ch. 12.5 - Assume that s is an arc length parameter for a...Ch. 12.5 - Assume that s is an arc length parameter for a...Ch. 12.5 - Prob. 61ESCh. 12.5 - (a) Use the chain rule and the first two...Ch. 12.5 - Use the formula in Exercise 62(d) to find the...Ch. 12.5 - Use the formula in Exercise 62(d) to find the...Ch. 12.5 - Use the formula in Exercise 62(d) to find the...Ch. 12.5 - Use the formula in Exercise 62(d) to find the...Ch. 12.5 - The accompanying figure is the graph of the radius...Ch. 12.6 - If r(t) is the position function of a particle,...Ch. 12.6 - If r(t) is the position function of a particle,...Ch. 12.6 - The tangential scalar component of acceleration is...Ch. 12.6 - The projectile motion model r(t)=12gt2+s0j+tv0...Ch. 12.6 - Prob. 1ESCh. 12.6 - Prob. 2ESCh. 12.6 - Prob. 3ESCh. 12.6 - Prob. 4ESCh. 12.6 - Find the velocity, speed, and acceleration at the...Ch. 12.6 - Find the velocity, speed, and acceleration at the...Ch. 12.6 - Find the velocity, speed, and acceleration at the...Ch. 12.6 - Find the velocity, speed, and acceleration at the...Ch. 12.6 - As illustrated in the accompanying figure, suppose...Ch. 12.6 - Suppose that a particle vibrates in such a way...Ch. 12.6 - What can you say about the trajectory of a...Ch. 12.6 - Prob. 12ESCh. 12.6 - Suppose that the position vector of a particle...Ch. 12.6 - Prob. 14ESCh. 12.6 - Suppose that the position function of a particle...Ch. 12.6 - Suppose that the position function of a particle...Ch. 12.6 - Prob. 17ESCh. 12.6 - Use the given information to find the position and...Ch. 12.6 - Prob. 19ESCh. 12.6 - Prob. 20ESCh. 12.6 - Find to the nearest degree, the angle between v...Ch. 12.6 - Prob. 22ESCh. 12.6 - (a) Suppose that at time t=t0 an electron has a...Ch. 12.6 - Suppose that the position function of a particle...Ch. 12.6 - Find the displacement and the distance travelled...Ch. 12.6 - Find the displacement and the distance travelled...Ch. 12.6 - Find the displacement and the distance travelled...Ch. 12.6 - Find the displacement and the distance traveled...Ch. 12.6 - The position vectors r1andr2 of two particles are...Ch. 12.6 - The position vectors r1andr2 of two particles are...Ch. 12.6 - Prob. 31ESCh. 12.6 - Prob. 32ESCh. 12.6 - Prob. 33ESCh. 12.6 - The position function of a particle is given. Use...Ch. 12.6 - Prob. 35ESCh. 12.6 - Prob. 36ESCh. 12.6 - In these exercises v and a are given at a certain...Ch. 12.6 - In these exercises v and a are given at a certain...Ch. 12.6 - The speed v of a particle at an arbitrary time t...Ch. 12.6 - The speed v of a particle at an arbitrary time t...Ch. 12.6 - The nuclear accelerator at the Enrico Fermi...Ch. 12.6 - Prob. 42ESCh. 12.6 - Prob. 43ESCh. 12.6 - Use the given information and Exercise 23 of...Ch. 12.6 - Use the given information to find the normal...Ch. 12.6 - Use the given information to find the normal...Ch. 12.6 - Determine whether the statement is true or false....Ch. 12.6 - Determine whether the statement is true or false....Ch. 12.6 - Determine whether the statement is true or false....Ch. 12.6 - Determine whether the statement is true or false....Ch. 12.6 - Derive Formula (18) from Formula (14).Ch. 12.6 - An automobile travels at a constant speed around a...Ch. 12.6 - If an automobile of mass m rounds a curve, then...Ch. 12.6 - A Shell is fired from ground level with a muzzle...Ch. 12.6 - A rock is thrown downward from the top of a...Ch. 12.6 - Solve Exercise 55 assuming that the rock is thrown...Ch. 12.6 - A shell is to be fired from ground level at an...Ch. 12.6 - A shell, fired from ground level at an elevation...Ch. 12.6 - Find two elevation angles that will enable a...Ch. 12.6 - A ball rolls off a table 4 ft high while moving at...Ch. 12.6 - As illustrated in the accompanying figure, a fire...Ch. 12.6 - What is the minimum initial velocity that will...Ch. 12.6 - As shown in the accompanying figure on the next...Ch. 12.6 - As illustrated in the accompanying figure, a train...Ch. 12.6 - A shell is fired from ground level at an elevation...Ch. 12.6 - A shell is fired from ground level with an...Ch. 12.6 - At time t=0 a baseball that is 5 ft above the...Ch. 12.6 - Repeat Exercise 67, assuming that the ball leaves...Ch. 12.6 - At time t=0 a skier leaves the end of a ski jump...Ch. 12.6 - At time t=0 a projectile is fired from a height h...Ch. 12.6 - Prob. 71ESCh. 12.7 - Let G denote the universal gravitational constant...Ch. 12.7 - Suppose that a mass m is in an orbit about a mass...Ch. 12.7 - For a planet in an elliptical orbit about the Sun,...Ch. 12.7 - Suppose that a mass m is an orbit about a mass M...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12.7 - In exercises that require numerical values, use...Ch. 12 - Prob. 1RECh. 12 - Describe the graph of the equation. r=23ti4tjCh. 12 - Describe the graph of the equation....Ch. 12 - Describe the graph of the equation....Ch. 12 - Describe the graph of the equation. r=2i+tj+t21kCh. 12 - Prob. 6RECh. 12 - Show that the graph of rt=tsinti+tj+tcostk lies on...Ch. 12 - Find parametric equations for the intersection of...Ch. 12 - In words, give a geometric description of the...Ch. 12 - Prob. 10RECh. 12 - Find parametric equations of the line tangent to...Ch. 12 - Suppose that r1tandr2t are smooth vector-valued...Ch. 12 - Evaluate costi+sintjdt.Ch. 12 - Evaluate 0/3cos3t,sin3tdt.Ch. 12 - Solve the vector initial-value problem...Ch. 12 - Solve the vector initial-value problem...Ch. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Find the arc length parametrization of the line...Ch. 12 - Find an arc length parametrization of the curve...Ch. 12 - Prob. 21RECh. 12 - Find T0,N0,andB0 for the curve...Ch. 12 - State the definition of "curvature" and explain...Ch. 12 - Suppose that rt is a smooth curve with r 0=iandr...Ch. 12 - Find the curvature of the curve at the stated...Ch. 12 - Find the curvature of the curve at the stated...Ch. 12 - Find the curvature of the curve at the stated...Ch. 12 - Find the curvature of the curve at the stated...Ch. 12 - Suppose that rt is the position function of a...Ch. 12 - (a) What does Theorem 12.2.8 tell you about the...Ch. 12 - As illustrated in the accompanying figure on the...Ch. 12 - If a particle of mass m has uniform circular...Ch. 12 - At time t=0 a particle at the origin of an...Ch. 12 - Prob. 34RECh. 12 - Use Formula (23) in Section 12.7 and refer to...Ch. 12 - As illustrated in the accompanying figure, the...Ch. 12 - A player throws a ball with an initial speed of 60...
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- ٣/١ B msl kd 180 Ka, Sin (1) I sin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 G 5005 1000 s = 1000-950 Copper bosses 5kW Rotor input 5 0.05 : loo kw 6) 1 /0001 ined sove in peaper I need a detailed solution on paper please وه اذا ميريد شرح الكتب فقط ١٥٠ DC 7) rotor a ' (y+xlny + xe*)dx + (xsiny + xlnx + dy = 0. Q1// Find the solution of: ( 357arrow_forward۳/۱ R₂ = X2 2) slots per pole per phase 3/31 B. 180 msl Kas Sin (I) 1sin() sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30): 0.866 4) Rotating 5) Synchronous speeds 120×50 looo G 1000-950 1000 Copper losses 5kw Rotor input 5 loo kw 0.05 6) 1 اذا ميريد شرح الكتب فقط look 7) rotor DC ined sove in peaper I need a detailed solution on paper please 0 64 Find the general solution of the following equations: QI//y(4)-16y= 0. Find the general solution of the following equations: Q2ll yll-4y/ +13y=esinx.arrow_forwardR₂ = X2 2) slots per pole per phase = 3/31 B-180 60 msl kd Kas Sin () 2 I sin (6) sin(30) Sin (30) اذا مريد شرح الكتب بس 0 بالفراغ 3 Cos (30) 0.866 4) Rotating ined sove in peaper 5) Synchronous speed s 120×50 6 s = 1000-950 1000 Copper losses 5kw Rotor input 5 0.05 6) 1 loo kw اذا ميريد شرح الكتب فقط Look 7) rotov DC I need a detailed solution on paper please 0 64 Solve the following equations: 0 Q1// Find the solution of: ( y • with y(0) = 1. dx x²+y²arrow_forward
- R₂ = X2 2) slots per pole per phase = 3/3 1 B-180-60 msl Ka Sin (1) Isin () sin(30) Sin (30) اذا ميريد شرح الكتب بس 0 بالفراغ 3) Cos (30) 0.866 4) Rotating 5) Synchronous speed, 120 x 50 s = 1000-950 1000 Copper losses 5kw Rotor input 5 6) 1 0.05 G 50105 loo kw اذا ميريد شرح الكتب فقط look 7) rotov DC ined sove in peaper I need a detailed solution on paper please 064 2- A hot ball (D=15 cm ) is cooled by forced air T.-30°C, the rate of heat transfer from the ball is 460.86 W. Take for the air -0.025 Wim °C and Nu=144.89, find the ball surface temperature a) 300 °C 16 b) 327 °C c) 376 °C d) None か = 750 01arrow_forwardDon't do 14. Please solve 19arrow_forwardPlease solve 14 and 15arrow_forward
- 1. Consider the following system of equations: x13x2 + 4x3 - 5x4 = 7 -2x13x2 + x3 - 6x4 = 7 x16x213x3 - 21x4 = 28 a) Solve the system. Write your solution in parametric and vector form. b) What is a geometric description of the solution. 7 c) Is v = 7 in the span of the set S= [28. 1 HE 3 -5 3 ·6 ? If it is, write v 6 as a linear combination of the vectors in S. Justify. d) How many solutions are there to the associated homogeneous system for the system above? Justify. e) Let A be the coefficient matrix from the system above. Find the set of all solutions to Ax = 0. f) Is there a solution to Ax=b for all b in R³? Justify.arrow_forward4. Suppose that A is made up of 5 column vectors in R³, and suppose that the rank(A)=3. a. How many solutions are there to Ax=0? Justify. b. What is a geometric description for the nullspace(A)? Justify. c. Do the column vectors of A span R³? Justify. d. Is A invertible? Justify.arrow_forward3. Suppose that A is 5 x 5 and rank(A)=4. Use this information to answer the following. a. Give a geometric description of nullspace(A). Justify. b. Is A invertible? Justify. c. Give a geometric description of the span of the column vectors of A. What space are the column vectors of A in? Justify. d. What is determinant of A? Justify.arrow_forward
- 2. Consider the matrix: A || 1 1 -3 14 2 1 01 4 1 2 2 -26 1 -3 1 5] a) What is rank(A)? b) Is A invertible? Justify. c) Find the nullspace(A). Justify. d) Is the trivial solution the only solution to Ax=0? Justify. e) What is the span of the column vectors of A? Justify.arrow_forwardE 5. Suppose that S={v € R²: v = [2x² - 3]}. Is S a subspace of R²? Prove or disprovearrow_forward6. Suppose that V1, V2 ER", show that span{v1, v2} is a subspace of Rn.arrow_forward
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