 12.2.1: (a) limt 3(t 2i + 2tj) =(b) lim t /4cost,sin t =
 12.2.2: Find r(t).(a) r(t) = (4 + 5t)i + (t t2)j(b) r(t) =1t, tan t,e2t
 12.2.3: Suppose that r1(0) = 3, 2, 1, r2(0) = 1, 2, 3,r1(0) = 0, 0, 0, and ...
 12.2.4: (a) 102t,t 2,sin t dt =(b) (ti 3t2j + etk)dt =
 12.2.5: 56 Determine whether r(t) is continuous at t = 0. Explainyour reaso...
 12.2.6: 56 Determine whether r(t) is continuous at t = 0. Explainyour reaso...
 12.2.7: Sketch the circle r(t) = costi + sin tj, and in each partdraw the v...
 12.2.8: Sketch the circle r(t) = costi sin tj, and in each partdraw the vec...
 12.2.9: 910 Find r (t). r(t) = 4i costj
 12.2.10: 910 Find r (t). r(t) = (tan1 t)i + t cost j t k
 12.2.11: 1114 Find the vector r(t0); then sketch the graph of r(t) in2space...
 12.2.12: 1114 Find the vector r(t0); then sketch the graph of r(t) in2space...
 12.2.13: 1114 Find the vector r(t0); then sketch the graph of r(t) in2space...
 12.2.14: 1114 Find the vector r(t0); then sketch the graph of r(t) in2space...
 12.2.15: 1516 Find the vector r(t0); then sketch the graph of r(t) in3space...
 12.2.16: 1516 Find the vector r(t0); then sketch the graph of r(t) in3space...
 12.2.17: 1718 Use a graphing utility to generate the graph of r(t) andthe gr...
 12.2.18: 1718 Use a graphing utility to generate the graph of r(t) andthe gr...
 12.2.19: 1922 Find parametric equations of the line tangent to the graphof r...
 12.2.20: 1922 Find parametric equations of the line tangent to the graphof r...
 12.2.21: 1922 Find parametric equations of the line tangent to the graphof r...
 12.2.22: 1922 Find parametric equations of the line tangent to the graphof r...
 12.2.23: 2326 Find a vector equation of the line tangent to the graphof r(t)...
 12.2.24: 2326 Find a vector equation of the line tangent to the graphof r(t)...
 12.2.25: 2326 Find a vector equation of the line tangent to the graphof r(t)...
 12.2.26: 2326 Find a vector equation of the line tangent to the graphof r(t)...
 12.2.27: Let r(t) = costi + sin tj + k. Find(a) limt 0(r(t) r(t)) (b) limt 0...
 12.2.28: Let r(t) = ti + t 2 j + t 3k. Findlimt 1r(t) (r(t) r(t))
 12.2.29: 2930 Calculateddt [r1(t) r2(t)] andddt [r1(t) r2(t)]first by differ...
 12.2.30: 2930 Calculateddt [r1(t) r2(t)] andddt [r1(t) r2(t)]first by differ...
 12.2.31: 3134 Evaluate the indefinite integral.(3i + 4tj)dt
 12.2.32: 3134 Evaluate the indefinite integral. t2i 2tj +1tkdt
 12.2.33: 3134 Evaluate the indefinite integral.tet, ln t dt 3
 12.2.34: 3134 Evaluate the indefinite integral.et, et, 3t2 dt3
 12.2.35: 3540 Evaluate the definite integral. /20cos 2t,sin 2t dt 36
 12.2.36: 3540 Evaluate the definite integral. 10(t 2i + t3 j)dt
 12.2.37: 3540 Evaluate the definite integral. 20ti + t2 j dt
 12.2.38: 3540 Evaluate the definite integral. 33(3 t)3/2, (3 + t)3/2, 1 dt3
 12.2.39: 3540 Evaluate the definite integral. 91(t 1/2i + t1/2 j)dt
 12.2.40: 3540 Evaluate the definite integral. 10(e2ti + et j + tk)dt
 12.2.41: 4144 TrueFalse Determine whether the statement is true orfalse. Exp...
 12.2.42: 4144 TrueFalse Determine whether the statement is true orfalse. Exp...
 12.2.43: 4144 TrueFalse Determine whether the statement is true orfalse. Exp...
 12.2.44: 4144 TrueFalse Determine whether the statement is true orfalse. Exp...
 12.2.45: 4548 Solve the vector initialvalue problem for y(t) by integrating...
 12.2.46: 4548 Solve the vector initialvalue problem for y(t) by integrating...
 12.2.47: 4548 Solve the vector initialvalue problem for y(t) by integrating...
 12.2.48: 4548 Solve the vector initialvalue problem for y(t) by integrating...
 12.2.49: (a) Find the points where the curver = ti + t2 j 3tkintersects the ...
 12.2.50: Find where the tangent line to the curver = e2ti + costj + 3 sin tk...
 12.2.51: 5152 Show that the graphs of r1(t) and r2(t) intersect at thepoint ...
 12.2.52: 5152 Show that the graphs of r1(t) and r2(t) intersect at thepoint ...
 12.2.53: Use Formula (7) to derive the differentiation formuladdt [r(t) r(t)...
 12.2.54: Let u = u(t), v = v(t), and w = w(t) be differentiablevectorvalued...
 12.2.55: Let u1, u2, u3, v1, v2, v3, w1, w2, and w3 be differentiablefunctio...
 12.2.56: Prove Theorem 12.2.6 for 2space.
 12.2.57: Derive Formulas (6) and (7) for 3space.
 12.2.58: Prove Theorem 12.2.9 for 2space.
 12.2.59: Writing Explain what it means for a vectorvalued functionr(t) to b...
 12.2.60: Writing Let r(t) = t 2, t 3 + 1 and define (t)to be the anglebetwee...
Solutions for Chapter 12.2: CALCULUS OF VECTORVALUED FUNCTIONS
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 12.2: CALCULUS OF VECTORVALUED FUNCTIONS
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. Since 60 problems in chapter 12.2: CALCULUS OF VECTORVALUED FUNCTIONS have been answered, more than 38387 students have viewed full stepbystep solutions from this chapter. Chapter 12.2: CALCULUS OF VECTORVALUED FUNCTIONS includes 60 full stepbystep solutions.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Elimination method
A method of solving a system of linear equations

Equation
A statement of equality between two expressions.

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Interval notation
Notation used to specify intervals, pp. 4, 5.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Inverse cosecant function
The function y = csc1 x

Length of an arrow
See Magnitude of an arrow.

Logistic regression
A procedure for fitting a logistic curve to a set of data

Natural logarithmic function
The inverse of the exponential function y = ex, denoted by y = ln x.

Natural logarithmic regression
A procedure for fitting a logarithmic curve to a set of data.

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Terminal side of an angle
See Angle.

Vertical translation
A shift of a graph up or down.

zaxis
Usually the third dimension in Cartesian space.