 12.2.1: In Exercises 16, sketch the plane curve represented by the vectorv...
 12.2.2: In Exercises 16, sketch the plane curve represented by the vectorv...
 12.2.3: In Exercises 16, sketch the plane curve represented by the vectorv...
 12.2.4: In Exercises 16, sketch the plane curve represented by the vectorv...
 12.2.5: In Exercises 16, sketch the plane curve represented by the vectorv...
 12.2.6: In Exercises 16, sketch the plane curve represented by the vectorv...
 12.2.7: Investigation Consider the vectorvalued function (a) Sketch the gr...
 12.2.8: Investigation Consider the vectorvalued function (a) Sketch the gr...
 12.2.9: In Exercises 9 and 10, (a) sketch the space curve represented by th...
 12.2.10: In Exercises 9 and 10, (a) sketch the space curve represented by th...
 12.2.11: In Exercises 1118, find rt.rt 6ti 7t k 2j t3kr
 12.2.12: In Exercises 1118, find rt.rt 1ti 16tjt
 12.2.13: In Exercises 1118, find rt.
 12.2.14: In Exercises 1118, find rt.rt 4t i t2t j ln t2krt
 12.2.15: In Exercises 1118, find rt.
 12.2.16: In Exercises 1118, find rt.rt sin t t cos t, cos t t sin t, t2r
 12.2.17: In Exercises 1118, find rt.rt t sin t, t cos t, t r
 12.2.18: In Exercises 1118, find rt.rt arcsin t, arccos t, 0r
 12.2.19: In Exercises 1926, find (a) and (b rt rt. rt t 2 tj 3i 12t2jrt
 12.2.20: In Exercises 1926, find (a) and (b rt rt. t t2 ti t rt t 2 tj 3i 1
 12.2.21: In Exercises 1926, find (a) and (b rt rt.
 12.2.22: In Exercises 1926, find (a) and (b rt rt.
 12.2.23: In Exercises 1926, find (a) and (b rt rt.rt 12 t2i tj 16t3kr
 12.2.24: In Exercises 1926, find (a) and (b rt rt.
 12.2.25: In Exercises 1926, find (a) and (b rt rt.rt cos t t sin t, sin t t ...
 12.2.26: In Exercises 1926, find (a) and (b rt rt.rt et, t2, tan tr
 12.2.27: In Exercises 27 and 28, a vectorvalued function and its graph are ...
 12.2.28: In Exercises 27 and 28, a vectorvalued function and its graph are ...
 12.2.29: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.30: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.31: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.32: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.33: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.34: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.35: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.36: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.37: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.38: In Exercises 2938, find the open interval(s) on which the curve giv...
 12.2.39: In Exercises 39 and 40, use the properties of the derivative to fin...
 12.2.40: In Exercises 39 and 40, use the properties of the derivative to fin...
 12.2.41: In Exercises 41 and 42, find (a) and (b) by differentiating the pro...
 12.2.42: In Exercises 41 and 42, find (a) and (b) by differentiating the pro...
 12.2.43: In Exercises 43 and 44, find the angle between and as a function of...
 12.2.44: In Exercises 43 and 44, find the angle between and as a function of...
 12.2.45: In Exercises 4548, use the definition of the derivative to find rt.
 12.2.46: In Exercises 4548, use the definition of the derivative to find rt.
 12.2.47: In Exercises 4548, use the definition of the derivative to find rt.
 12.2.48: In Exercises 4548, use the definition of the derivative to find rt.
 12.2.49: In Exercises 4956, find the indefinite integral2ti j k dt i
 12.2.50: In Exercises 4956, find the indefinite integral
 12.2.51: In Exercises 4956, find the indefinite integral dt 1ti j t 32 k dt
 12.2.52: In Exercises 4956, find the indefinite integralln ti1t j k dt
 12.2.53: In Exercises 4956, find the indefinite integral2t 1i 4t3j 3t k dt
 12.2.54: In Exercises 4956, find the indefinite integralet i sin tj cos tk dt
 12.2.55: In Exercises 4956, find the indefinite integralsec2 ti11 t2 j dt
 12.2.56: In Exercises 4956, find the indefinite integralet sin ti et cos tj dt
 12.2.57: In Exercises 5762, evaluate the definite integral.
 12.2.58: In Exercises 5762, evaluate the definite integral.
 12.2.59: In Exercises 5762, evaluate the definite integral.20a cos ti a sin ...
 12.2.60: In Exercises 5762, evaluate the definite integral.sec t tan ti tan ...
 12.2.61: In Exercises 5762, evaluate the definite integral.ti et j tetk dt
 12.2.62: In Exercises 5762, evaluate the definite integral.30ti t2 j dt
 12.2.63: In Exercises 6368, find for the given conditions.t 4e r0 2i 2t
 12.2.64: In Exercises 6368, find for the given conditions.rt 3t r0 i 2j 2j 6
 12.2.65: In Exercises 6368, find for the given conditions.rt 32j, r0 6003i 6...
 12.2.66: In Exercises 6368, find for the given conditions.rt 4 cos tj 3 sin ...
 12.2.67: In Exercises 6368, find for the given conditions.rt te i j k t
 12.2.68: In Exercises 6368, find for the given conditions.rt r1 2i 11
 12.2.69: State the definition of the derivative of a vectorvalued function....
 12.2.70: How do you find the integral of a vectorvalued function?
 12.2.71: The three components of the derivative of the vectorvalued functio...
 12.2.72: The three components of the derivative of the vectorvalued functio...
 12.2.73: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.74: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.75: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.76: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.77: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.78: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.79: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.80: In Exercises 7380, prove the property. In each case, assume r, u, a...
 12.2.81: Particle Motion A particle moves in the xyplane along the curve re...
 12.2.82: Particle Motion A particle moves in the yzplane along the curve re...
 12.2.83: True or False? In Exercises 8386, determine whether the statement i...
 12.2.84: True or False? In Exercises 8386, determine whether the statement i...
 12.2.85: True or False? In Exercises 8386, determine whether the statement i...
 12.2.86: True or False? In Exercises 8386, determine whether the statement i...
 12.2.87: Consider the vectorvalued function Show that and are always perpen...
Solutions for Chapter 12.2: Differentiation and Integration of VectorValued Functions
Full solutions for Calculus: Early Transcendental Functions  4th Edition
ISBN: 9780618606245
Solutions for Chapter 12.2: Differentiation and Integration of VectorValued Functions
Get Full SolutionsChapter 12.2: Differentiation and Integration of VectorValued Functions includes 87 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus: Early Transcendental Functions , edition: 4. Since 87 problems in chapter 12.2: Differentiation and Integration of VectorValued Functions have been answered, more than 39113 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendental Functions was written by and is associated to the ISBN: 9780618606245.

Circle
A set of points in a plane equally distant from a fixed point called the center

Commutative properties
a + b = b + a ab = ba

Compound interest
Interest that becomes part of the investment

Constant
A letter or symbol that stands for a specific number,

Cotangent
The function y = cot x

Difference of functions
(ƒ  g)(x) = ƒ(x)  g(x)

Direct variation
See Power function.

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

Halfplane
The graph of the linear inequality y ? ax + b, y > ax + b y ? ax + b, or y < ax + b.

Measure of spread
A measure that tells how widely distributed data are.

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Obtuse triangle
A triangle in which one angle is greater than 90°.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Rectangular coordinate system
See Cartesian coordinate system.

Sample survey
A process for gathering data from a subset of a population, usually through direct questioning.

Velocity
A vector that specifies the motion of an object in terms of its speed and direction.

xintercept
A point that lies on both the graph and the xaxis,.

xzplane
The points x, 0, z in Cartesian space.

yzplane
The points (0, y, z) in Cartesian space.