 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
 12.2.12: In Exercises 1118, find
 12.2.13: In Exercises 1118, find
 12.2.14: In Exercises 1118, find
 12.2.15: In Exercises 1118, find
 12.2.16: In Exercises 1118, find
 12.2.17: In Exercises 1118, find
 12.2.18: In Exercises 1118, find
 12.2.19: In Exercises 1926, find (a) and (b)
 12.2.20: In Exercises 1926, find (a) and (b)
 12.2.21: In Exercises 1926, find (a) and (b)
 12.2.22: In Exercises 1926, find (a) and (b)
 12.2.23: In Exercises 1926, find (a) and (b)
 12.2.24: In Exercises 1926, find (a) and (b)
 12.2.25: In Exercises 1926, find (a) and (b)
 12.2.26: In Exercises 1926, find (a) and (b)
 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
 12.2.46: In Exercises 4548, use the definition of the derivative to find
 12.2.47: In Exercises 4548, use the definition of the derivative to find
 12.2.48: In Exercises 4548, use the definition of the derivative to find
 12.2.49: In Exercises 4956, find the indefinite integral.
 12.2.50: In Exercises 4956, find the indefinite integral.
 12.2.51: In Exercises 4956, find the indefinite integral.
 12.2.52: In Exercises 4956, find the indefinite integral.
 12.2.53: In Exercises 4956, find the indefinite integral.
 12.2.54: In Exercises 4956, find the indefinite integral.
 12.2.55: In Exercises 4956, find the indefinite integral.
 12.2.56: In Exercises 4956, find the indefinite integral.
 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.
 12.2.60: In Exercises 5762, evaluate the definite integral.
 12.2.61: In Exercises 5762, evaluate the definite integral.
 12.2.62: In Exercises 5762, evaluate the definite integral.
 12.2.63: In Exercises 6368, find for the given conditions.
 12.2.64: In Exercises 6368, find for the given conditions.
 12.2.65: In Exercises 6368, find for the given conditions.
 12.2.66: In Exercises 6368, find for the given conditions.
 12.2.67: In Exercises 6368, find for the given conditions.
 12.2.68: In Exercises 6368, find for the given conditions.
 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: How do you find the integral of a vectorvalued function?
 12.2.72: How do you find the integral of a vectorvalued function?
 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: If is a constant, then
 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  8th Edition
ISBN: 9780618502981
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 textbook survival guide was created for the textbook: Calculus, edition: 8. Since 87 problems in chapter 12.2: Differentiation and Integration of VectorValued Functions have been answered, more than 78159 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Calculus was written by and is associated to the ISBN: 9780618502981.

Component form of a vector
If a vector’s representative in standard position has a terminal point (a,b) (or (a, b, c)) , then (a,b) (or (a, b, c)) is the component form of the vector, and a and b are the horizontal and vertical components of the vector (or a, b, and c are the x, y, and zcomponents of the vector, respectively)

Domain of a function
The set of all input values for a function

Even function
A function whose graph is symmetric about the yaxis for all x in the domain of ƒ.

Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Initial side of an angle
See Angle.

Interquartile range
The difference between the third quartile and the first quartile.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Mean (of a set of data)
The sum of all the data divided by the total number of items

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Parameter
See Parametric equations.

Pointslope form (of a line)
y  y1 = m1x  x 12.

Polar coordinate system
A coordinate system whose ordered pair is based on the directed distance from a central point (the pole) and the angle measured from a ray from the pole (the polar axis)

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Power regression
A procedure for fitting a curve y = a . x b to a set of data.

Principle of mathematical induction
A principle related to mathematical induction.

Real zeros
Zeros of a function that are real numbers.

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Terminal point
See Arrow.

Window dimensions
The restrictions on x and y that specify a viewing window. See Viewing window.