 11.6.1: What is the derivative of r1t2 = 8f 1t2, g1t2, h1t29?
 11.6.2: Explain the geometric meaning of r_1t2.
 11.6.3: Given a tangent vector on an oriented curve, how do you find the un...
 11.6.4: Compute r_1t2 when r1t2 = 8t10, 8t, cos t9.
 11.6.5: How do you find the indefinite integral of r1t2 = 8f 1t2, g1t2, h1t29?
 11.6.6: How do you evaluate 1 b a r1t2 dt?
 11.6.7: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.8: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.9: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.10: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.11: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.12: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.13: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.14: 714. Derivatives of vectorvalued functions Differentiate the follo...
 11.6.15: 1520. Tangent vectors Find a tangent vector at the given value of t...
 11.6.16: 1520. Tangent vectors Find a tangent vector at the given value of t...
 11.6.17: 1520. Tangent vectors Find a tangent vector at the given value of t...
 11.6.18: 1520. Tangent vectors Find a tangent vector at the given value of t...
 11.6.19: 1520. Tangent vectors Find a tangent vector at the given value of t...
 11.6.20: 1520. Tangent vectors Find a tangent vector at the given value of t...
 11.6.21: 2126. Unit tangent vectors Find the unit tangent vector for the fol...
 11.6.22: 2126. Unit tangent vectors Find the unit tangent vector for the fol...
 11.6.23: 2126. Unit tangent vectors Find the unit tangent vector for the fol...
 11.6.24: 2126. Unit tangent vectors Find the unit tangent vector for the fol...
 11.6.25: 2126. Unit tangent vectors Find the unit tangent vector for the fol...
 11.6.26: 2126. Unit tangent vectors Find the unit tangent vector for the fol...
 11.6.27: 2730. Unit tangent vectors at a point Find the unit tangent vector ...
 11.6.28: 2730. Unit tangent vectors at a point Find the unit tangent vector ...
 11.6.29: 2730. Unit tangent vectors at a point Find the unit tangent vector ...
 11.6.30: 2730. Unit tangent vectors at a point Find the unit tangent vector ...
 11.6.31: 3136. Derivative rules Let u1t2 = 2t3 i + 1t 2  12 j  8k and v1t2...
 11.6.32: 3136. Derivative rules Let u1t2 = 2t3 i + 1t 2  12 j  8k and v1t2...
 11.6.33: 3136. Derivative rules Let u1t2 = 2t3 i + 1t 2  12 j  8k and v1t2...
 11.6.34: 3136. Derivative rules Let u1t2 = 2t3 i + 1t 2  12 j  8k and v1t2...
 11.6.35: 3136. Derivative rules Let u1t2 = 2t3 i + 1t 2  12 j  8k and v1t2...
 11.6.36: 3136. Derivative rules Let u1t2 = 2t3 i + 1t 2  12 j  8k and v1t2...
 11.6.37: 3740. Derivative rules Compute the following derivatives. d dt 1t 2...
 11.6.38: 3740. Derivative rules Compute the following derivatives. d dt 11t3...
 11.6.39: 3740. Derivative rules Compute the following derivatives. d dt 113t...
 11.6.40: 3740. Derivative rules Compute the following derivatives. d dt 11t3...
 11.6.41: 4146. Higherorder derivatives Compute r1t2 and r1t2 for the follow...
 11.6.42: 4146. Higherorder derivatives Compute r1t2 and r1t2 for the follow...
 11.6.43: 4146. Higherorder derivatives Compute r1t2 and r1t2 for the follow...
 11.6.44: 4146. Higherorder derivatives Compute r1t2 and r1t2 for the follow...
 11.6.45: 4146. Higherorder derivatives Compute r1t2 and r1t2 for the follow...
 11.6.46: 4146. Higherorder derivatives Compute r1t2 and r1t2 for the follow...
 11.6.47: 4752. Indefinite integrals Compute the indefinite integral of the f...
 11.6.48: 4752. Indefinite integrals Compute the indefinite integral of the f...
 11.6.49: 4752. Indefinite integrals Compute the indefinite integral of the f...
 11.6.50: 4752. Indefinite integrals Compute the indefinite integral of the f...
 11.6.51: 4752. Indefinite integrals Compute the indefinite integral of the f...
 11.6.52: 4752. Indefinite integrals Compute the indefinite integral of the f...
 11.6.53: 5358. Finding r from r Find the function r that satisfies the given...
 11.6.54: 5358. Finding r from r Find the function r that satisfies the given...
 11.6.55: 5358. Finding r from r Find the function r that satisfies the given...
 11.6.56: 5358. Finding r from r Find the function r that satisfies the given...
 11.6.57: 5358. Finding r from r Find the function r that satisfies the given...
 11.6.58: 5358. Finding r from r Find the function r that satisfies the given...
 11.6.59: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.60: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.61: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.62: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.63: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.64: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.65: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.66: 5966. Definite integrals Evaluate the following definite integrals....
 11.6.67: Explain why or why not Determine whether the following statements a...
 11.6.68: 6871. Tangent lines Suppose the vectorvalued function r1t2 = 8f 1t...
 11.6.69: 6871. Tangent lines Suppose the vectorvalued function r1t2 = 8f 1t...
 11.6.70: 6871. Tangent lines Suppose the vectorvalued function r1t2 = 8f 1t...
 11.6.71: 6871. Tangent lines Suppose the vectorvalued function r1t2 = 8f 1t...
 11.6.72: 7277. Derivative rules Let u1t2 = 81, t, t 29, v1t2 = 8t 2, 2t, 19...
 11.6.73: 7277. Derivative rules Let u1t2 = 81, t, t 29, v1t2 = 8t 2, 2t, 19...
 11.6.74: 7277. Derivative rules Let u1t2 = 81, t, t 29, v1t2 = 8t 2, 2t, 19...
 11.6.75: 7277. Derivative rules Let u1t2 = 81, t, t 29, v1t2 = 8t 2, 2t, 19...
 11.6.76: 7277. Derivative rules Let u1t2 = 81, t, t 29, v1t2 = 8t 2, 2t, 19...
 11.6.77: 7277. Derivative rules Let u1t2 = 81, t, t 29, v1t2 = 8t 2, 2t, 19...
 11.6.78: Consider the circle r1t2 = 8a cos t, a sin t9, for 0 t 2p, where a ...
 11.6.79: Consider the parabola r1t2 = 8at 2 + 1, t9, for  _ 6 t 6 _, where ...
 11.6.80: Consider the curve r1t2 = 81t, 1, t9, for t 7 0. Find all points on...
 11.6.81: Consider the helix r1t2 = 8cos t, sin t, t9, for  _ 6 t 6 _. Find ...
 11.6.82: Consider the ellipse r1t2 = 82 cos t, 8 sin t, 09, for 0 t 2p. Find...
 11.6.83: Give two families of curves in _3 for which r and r_ are parallel f...
 11.6.84: Derivative rules Suppose u and v are differentiable functions at t ...
 11.6.85: Vectors r and r_ for lines a. If r1t2 = 8at, bt, ct9 with 8a, b, c9...
 11.6.86: Proof of Sum Rule By expressing u and v in terms of their component...
 11.6.87: Proof of Product Rule By expressing u in terms of its components, p...
 11.6.88: Proof of Cross Product Rule Prove that d dt 1u1t2 * v1t22 = u_1t2 *...
 11.6.89: Cusps and noncusps a. Graph the curve r1t2 = 8t3, t39. Show that r_...
 11.6.90: Motion on a sphere Prove that r describes a curve that lies on the ...
Solutions for Chapter 11.6: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 11.6
Get Full SolutionsSince 90 problems in chapter 11.6 have been answered, more than 39493 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 11.6 includes 90 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345.

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.

Annuity
A sequence of equal periodic payments.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Composition of functions
(f ? g) (x) = f (g(x))

Horizontal translation
A shift of a graph to the left or right.

Inferential statistics
Using the science of statistics to make inferences about the parameters in a population from a sample.

Line of travel
The path along which an object travels

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.

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

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Present value of an annuity T
he net amount of your money put into an annuity.

Quartic regression
A procedure for fitting a quartic function to a set of data.

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Semiperimeter of a triangle
Onehalf of the sum of the lengths of the sides of a triangle.

Sinusoidal regression
A procedure for fitting a curve y = a sin (bx + c) + d to a set of data

Slopeintercept form (of a line)
y = mx + b

Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.