- 12.1: In Exercises 14, (a) find the domain of and (b) determine the value...
- 12.2: In Exercises 14, (a) find the domain of and (b) determine the value...
- 12.3: In Exercises 14, (a) find the domain of and (b) determine the value...
- 12.4: In Exercises 14, (a) find the domain of and (b) determine the value...
- 12.5: In Exercises 5 and 6, evaluate (if possible) the vector-valued func...
- 12.6: In Exercises 5 and 6, evaluate (if possible) the vector-valued func...
- 12.7: In Exercises 7 and 8, sketch the plane curve represented by the vec...
- 12.8: In Exercises 7 and 8, sketch the plane curve represented by the vec...
- 12.9: In Exercises 914, use a computer algebra system to graph the space ...
- 12.10: In Exercises 914, use a computer algebra system to graph the space ...
- 12.11: In Exercises 914, use a computer algebra system to graph the space ...
- 12.12: In Exercises 914, use a computer algebra system to graph the space ...
- 12.13: In Exercises 914, use a computer algebra system to graph the space ...
- 12.14: In Exercises 914, use a computer algebra system to graph the space ...
- 12.15: In Exercises 15 and 16, find vector-valued functions forming the bo...
- 12.16: In Exercises 15 and 16, find vector-valued functions forming the bo...
- 12.17: A particle moves on a straight-line path that passes through the po...
- 12.18: The outer edge of a spiral staircase is in the shape of a helix of ...
- 12.19: In Exercises 19 and 20, sketch the space curve represented by the i...
- 12.20: In Exercises 19 and 20, sketch the space curve represented by the i...
- 12.21: In Exercises 21 and 22, evaluate the limit.limt4 t i 4 t j k
- 12.22: In Exercises 21 and 22, evaluate the limit.LImt0 sin 2tti et j et k
- 12.23: In Exercises 23 and 24, find the following.
- 12.24: In Exercises 23 and 24, find the following.
- 12.25: Writing The and components of the derivative of the vector-valued f...
- 12.26: Writing The component of the derivative of the vectorvalued functio...
- 12.27: In Exercises 2730, find the indefinite integralcos t i t cos tj dt
- 12.28: In Exercises 2730, find the indefinite integralln t i t ln tj k dt
- 12.29: In Exercises 2730, find the indefinite integralcos t i sin tj t k dt
- 12.30: In Exercises 2730, find the indefinite integraltj t 2 k i tj t k dt
- 12.31: In Exercises 3134, evaluate the definite integral.223t i 2t 2 j t 3...
- 12.32: In Exercises 3134, evaluate the definite integral.t j t sin tk dt
- 12.33: In Exercises 3134, evaluate the definite integral.et2 i 3t2j k dt
- 12.34: In Exercises 3134, evaluate the definite integral.11t3i arcsin tj t...
- 12.35: In Exercises 35 and 36, find for the given conditions.rt 2t i e r0 ...
- 12.36: In Exercises 35 and 36, find for the given conditions.rt sec t i ta...
- 12.37: In Exercises 37 40, the position vector describes the path of an ob...
- 12.38: In Exercises 37 40, the position vector describes the path of an ob...
- 12.39: In Exercises 37 40, the position vector describes the path of an ob...
- 12.40: In Exercises 37 40, the position vector describes the path of an ob...
- 12.41: Linear Approximation In Exercises 41 and 42, find a set of parametr...
- 12.42: Linear Approximation In Exercises 41 and 42, find a set of parametr...
- 12.43: Projectile Motion In Exercises 43 46, use the model for projectile ...
- 12.44: Projectile Motion In Exercises 43 46, use the model for projectile ...
- 12.45: Projectile Motion In Exercises 43 46, use the model for projectile ...
- 12.46: Projectile Motion In Exercises 43 46, use the model for projectile ...
- 12.47: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.48: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.49: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.50: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.51: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.52: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.53: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.54: In Exercises 4754, find the velocity, speed, and acceleration at ti...
- 12.55: In Exercises 55 and 56, find a set of parametric equations for the ...
- 12.56: In Exercises 55 and 56, find a set of parametric equations for the ...
- 12.57: Satellite Orbit Find the speed necessary for a satellite to maintai...
- 12.58: Centripetal Force An automobile in a circular traffic exchange is t...
- 12.59: In Exercises 5962, sketch the plane curve and find its length over ...
- 12.60: In Exercises 5962, sketch the plane curve and find its length over ...
- 12.61: In Exercises 5962, sketch the plane curve and find its length over ...
- 12.62: In Exercises 5962, sketch the plane curve and find its length over ...
- 12.63: In Exercises 6366, sketch the space curve and find its length over ...
- 12.64: In Exercises 6366, sketch the space curve and find its length over ...
- 12.65: In Exercises 6366, sketch the space curve and find its length over ...
- 12.66: In Exercises 6366, sketch the space curve and find its length over ...
- 12.67: In Exercises 6770, find the curvature of the curve.rt 3ti 2tj
- 12.68: In Exercises 6770, find the curvature of the curve.rt 2t i 3t
- 12.69: In Exercises 6770, find the curvature of the curve.rt 2ti 12t2j t2k
- 12.70: In Exercises 6770, find the curvature of the curve.rt 2ti 5 cos tj ...
- 12.71: In Exercises 71 and 72, find the curvature of the curve at point Pr...
- 12.72: In Exercises 71 and 72, find the curvature of the curve at point Pt...
- 12.73: In Exercises 7376, find the curvature and radius of curvature of th...
- 12.74: In Exercises 7376, find the curvature and radius of curvature of th...
- 12.75: In Exercises 7376, find the curvature and radius of curvature of th...
- 12.76: In Exercises 7376, find the curvature and radius of curvature of th...
- 12.77: Writing A civil engineer designs a highway as shown in the figure. ...
- 12.78: A line segment extends horizontally to the left from the point and ...
Solutions for Chapter 12: Vector-Valued Functions
Full solutions for Calculus | 9th Edition
ISBN: 9780547167022
Solutions for Chapter 12
12
5
Calculus was written by and is associated to the ISBN: 9780547167022. This expansive textbook survival guide covers the following chapters and their solutions. Since 78 problems in chapter 12: Vector-Valued Functions have been answered, more than 36227 students have viewed full step-by-step solutions from this chapter. Chapter 12: Vector-Valued Functions includes 78 full step-by-step solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9.
Key Calculus Terms and definitions covered in this textbook
-
Acute angle
An angle whose measure is between 0° and 90°
-
Arrow
The notation PQ denoting the directed line segment with initial point P and terminal point Q.
-
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.
-
Composition of functions
(f ? g) (x) = f (g(x))
-
Conic section (or conic)
A curve obtained by intersecting a double-napped right circular cone with a plane
-
Direction of an arrow
The angle the arrow makes with the positive x-axis
-
Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant
-
Geometric sequence
A sequence {an}in which an = an-1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.
-
Higher-degree polynomial function
A polynomial function whose degree is ? 3
-
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
-
Initial point
See Arrow.
-
Initial side of an angle
See Angle.
-
Line graph
A graph of data in which consecutive data points are connected by line segments
-
Mean (of a set of data)
The sum of all the data divided by the total number of items
-
Root of an equation
A solution.
-
Row operations
See Elementary row operations.
-
Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n - 12d4,
-
Terms of a sequence
The range elements of a sequence.
-
Translation
See Horizontal translation, Vertical translation.
-
Unit vector
Vector of length 1.