 12.1.1: In Exercises 18, find the domain of the vectorvalued function.
 12.1.2: In Exercises 18, find the domain of the vectorvalued function.
 12.1.3: In Exercises 18, find the domain of the vectorvalued function.
 12.1.4: In Exercises 18, find the domain of the vectorvalued function.
 12.1.5: In Exercises 18, find the domain of the vectorvalued function.
 12.1.6: In Exercises 18, find the domain of the vectorvalued function.
 12.1.7: In Exercises 18, find the domain of the vectorvalued function.
 12.1.8: In Exercises 18, find the domain of the vectorvalued function.
 12.1.9: In Exercises 912, evaluate (if possible) the vectorvalued function...
 12.1.10: In Exercises 912, evaluate (if possible) the vectorvalued function...
 12.1.11: In Exercises 912, evaluate (if possible) the vectorvalued function...
 12.1.12: In Exercises 912, evaluate (if possible) the vectorvalued function...
 12.1.13: In Exercises 13 and 14, find
 12.1.14: In Exercises 13 and 14, find
 12.1.15: Think About It In Exercises 15 and 16, find Is the result a vector...
 12.1.16: Think About It In Exercises 15 and 16, find Is the result a vector...
 12.1.17: In Exercises 1720, match the equation with its graph. [The graphs a...
 12.1.18: In Exercises 1720, match the equation with its graph. [The graphs a...
 12.1.19: In Exercises 1720, match the equation with its graph. [The graphs a...
 12.1.20: In Exercises 1720, match the equation with its graph. [The graphs a...
 12.1.21: Think About It The four figures below are graphs of the vectorvalu...
 12.1.22: Sketch three graphs of the vectorvalued function as viewed from ea...
 12.1.23: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.24: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.25: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.26: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.27: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.28: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.29: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.30: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.31: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.32: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.33: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.34: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.35: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.36: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.37: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.38: In Exercises 2338, sketch the curve represented by the vectorvalued...
 12.1.39: In Exercises 3942, use a computer algebra system to graph the vecto...
 12.1.40: In Exercises 3942, use a computer algebra system to graph the vecto...
 12.1.41: In Exercises 3942, use a computer algebra system to graph the vecto...
 12.1.42: In Exercises 3942, use a computer algebra system to graph the vecto...
 12.1.43: Think About It In Exercises 43 and 44, use a computer algebra syste...
 12.1.44: Think About It In Exercises 43 and 44, use a computer algebra syste...
 12.1.45: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.46: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.47: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.48: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.49: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.50: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.51: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.52: In Exercises 4552, represent the plane curve by a vectorvalued func...
 12.1.53: A particle moves on a straightline path that passes through the po...
 12.1.54: The outer edge of a playground slide is in the shape of a helix of ...
 12.1.55: In Exercises 5558, find vectorvalued functions forming the boundar...
 12.1.56: In Exercises 5558, find vectorvalued functions forming the boundar...
 12.1.57: In Exercises 5558, find vectorvalued functions forming the boundar...
 12.1.58: In Exercises 5558, find vectorvalued functions forming the boundar...
 12.1.59: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.60: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.61: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.62: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.63: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.64: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.65: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.66: In Exercises 5966, sketch the space curve represented by the inters...
 12.1.67: Show that the vectorvalued function lies on the cone Sketch the cu...
 12.1.68: Show that the vectorvalued function lies on the cone Sketch the cu...
 12.1.69: In Exercises 6974, evaluate the limit.
 12.1.70: In Exercises 6974, evaluate the limit.
 12.1.71: In Exercises 6974, evaluate the limit.
 12.1.72: In Exercises 6974, evaluate the limit.
 12.1.73: In Exercises 6974, evaluate the limit.
 12.1.74: In Exercises 6974, evaluate the limit.
 12.1.75: In Exercises 7580, determine the interval(s) on which the vectorva...
 12.1.76: In Exercises 7580, determine the interval(s) on which the vectorva...
 12.1.77: In Exercises 7580, determine the interval(s) on which the vectorva...
 12.1.78: In Exercises 7580, determine the interval(s) on which the vectorva...
 12.1.79: In Exercises 7580, determine the interval(s) on which the vectorva...
 12.1.80: In Exercises 7580, determine the interval(s) on which the vectorva...
 12.1.81: State the definition of a vectorvalued function in the plane and i...
 12.1.82: If is a vectorvalued function, is the graph of the vectorvalued fu...
 12.1.83: Consider the vectorvalued function Write a vectorvalued function ...
 12.1.84: Consider the vectorvalued function Write a vectorvalued function ...
 12.1.85: Let and be vectorvalued functions whose limits exist as Prove that
 12.1.86: Let and be vectorvalued functions whose limits exist as Prove that
 12.1.87: Prove that if is a vectorvalued function that is continuous at the...
 12.1.88: Verify that the converse of Exercise 87 is not true by finding a ve...
 12.1.89: True or False? In Exercises 8992, determine whether the statement i...
 12.1.90: True or False? In Exercises 8992, determine whether the statement i...
 12.1.91: True or False? In Exercises 8992, determine whether the statement i...
 12.1.92: True or False? In Exercises 8992, determine whether the statement i...
Solutions for Chapter 12.1: VectorValued Functions
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 12.1: VectorValued Functions
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780618502981. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 12.1: VectorValued Functions includes 92 full stepbystep solutions. Since 92 problems in chapter 12.1: VectorValued Functions have been answered, more than 76558 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus, edition: 8.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Cosine
The function y = cos x

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

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Imaginary part of a complex number
See Complex number.

Leaf
The final digit of a number in a stemplot.

Negative linear correlation
See Linear correlation.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Principal nth root
If bn = a, then b is an nth root of a. If bn = a and a and b have the same sign, b is the principal nth root of a (see Radical), p. 508.

Probability distribution
The collection of probabilities of outcomes in a sample space assigned by a probability function.

Right triangle
A triangle with a 90° angle.

Solve an equation or inequality
To find all solutions of the equation or inequality

Square matrix
A matrix whose number of rows equals the number of columns.

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Third quartile
See Quartile.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.

Vector equation for a line in space
The line through P0(x 0, y0, z0) in the direction of the nonzero vector V = <a, b, c> has vector equation r = r0 + tv , where r = <x,y,z>.

Zero factorial
See n factorial.