- 13.1: Determine the domains of the vector-valued functions. (a) r1(t) = t...
- 13.2: Sketch the paths r1() = , cos and r2() = cos , in the xy-plane. 3.
- 13.3: Find a vector parametrization of the intersection of the surfaces x...
- 13.4: Find a vector parametrization using trigonometric functions of the ...
- 13.5: In Exercises 510, calculate the derivative indicated. 5. r (t), r(t...
- 13.6: In Exercises 510, calculate the derivative indicated.r (t), r(t) = ...
- 13.7: In Exercises 510, calculate the derivative indicated.r (0), r(t) = ...
- 13.8: In Exercises 510, calculate the derivative indicated.r (3), r(t) = ...
- 13.9: In Exercises 510, calculate the derivative indicated.d dt et 1,t,t2 1
- 13.10: In Exercises 510, calculate the derivative indicated.d d r(cos ), r...
- 13.11: In Exercises 1114, calculate the derivative at t = 3, assuming that...
- 13.12: In Exercises 1114, calculate the derivative at t = 3, assuming that...
- 13.13: In Exercises 1114, calculate the derivative at t = 3, assuming that...
- 13.14: In Exercises 1114, calculate the derivative at t = 3, assuming that...
- 13.15: Calculate 3 0 4t + 3, t2, 4t 3 dt. 16
- 13.16: Calculate 0 sin ,, cos 2 d. 17
- 13.17: A particle located at (1, 1, 0) at time t = 0 follows a path whose ...
- 13.18: Find the vector-valued function r(t) = x(t), y(t) in R2 satisfying ...
- 13.19: Calculate r(t), assuming that r (t) = 4 16t, 12t 2 t , r (0) = 1, 0...
- 13.20: Solve r (t) = t2 1, t + 1, t3 subject to the initial conditions r(0...
- 13.21: Compute the length of the path r(t) = sin 2t, cos 2t, 3t 1 for 1 t 3 2
- 13.22: Express the length of the path r(t) = ln t,t,et for 1 t 2 as a defi...
- 13.23: Find an arc length parametrization of a helix of height 20 cm that ...
- 13.24: Find the minimum speed of a particle with trajectory r(t)= (t,et-3,...
- 13.25: A projectile fired at an angle of 60 lands 400 m away. What was its...
- 13.26: A specially trained mouse runs counterclockwise in a circle of radi...
- 13.27: During a short time interval [0.5, 1.5], the path of an unmanned sp...
- 13.28: A force F = 12t + 4, 8 24t (in newtons) acts on a 2-kg mass. Find t...
- 13.29: Find the unit tangent vector to r(t) = sin t,t, cost at t = .
- 13.30: Find the unit tangent vector to r(t) = t2, tan1 t,t at t = 1. 3
- 13.31: Calculate (1) for r(t) = ln t,t. 3
- 13.32: Calculate 4 for r(t) = tan t,sec t, cost. I
- 13.33: In Exercises 33 and 34, write the acceleration vector a at the poin...
- 13.34: r(t) = t 2, 2t t 2, t , t = 2 3
- 13.35: At a certain time t0, the path of a moving particle is tangent to t...
- 13.36: Parametrize the osculating circle to y = x2 x3 at x = 1.
- 13.37: Parametrize the osculating circle to y = x at x = 4.
- 13.38: Let r(t) = cost,sin t, 2t. (a) Find T, N, and B at the point corres...
- 13.39: Let r(t) = ln t,t, t2 2 . Find the equation of the osculating plane...
- 13.40: If a planet has zero mass (m = 0), then Newtons laws of motion redu...
- 13.41: Suppose the orbit of a planet is an ellipse of eccentricity e = c/a...
- 13.42: The period of Mercury is approximately 88 days, and its orbit has e...
Solutions for Chapter 13: CALCULUS OF VECTOR-VALUED FUNCTIONS
Full solutions for Calculus: Early Transcendentals | 3rd Edition
Absolute value of a complex number
The absolute value of the complex number z = a + b is given by ?a2+b2; also, the length of the segment from the origin to z in the complex plane.
Axis of symmetry
See Line of symmetry.
Measure of the clockwise angle that the line of travel makes with due north
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively
See Polynomial function
Facts collected for statistical purposes (singular form is datum)
The process of utilizing general information to prove a specific hypothesis
The gathering and processing of numerical information
a(b + c) = ab + ac and related properties
The measure of an angle in degrees, minutes, and seconds
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1
Using the science of statistics to make inferences about the parameters in a population from a sample.
A function whose domain is the set of all natural numbers.
Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I
See Right circular cone.
A function in which each element of the range corresponds to exactly one element in the domain
Standard form: equation of a circle
(x - h)2 + (y - k2) = r 2
Trigonometric form of a complex number
r(cos ? + i sin ?)
A point that lies on both the graph and the x-axis,.