 13.2.1: The figure shows a curve given by a vector function . j k (a) Draw ...
 13.2.2: (a) Make a large sketch of the curve described by the vector functi...
 13.2.3: (a) Sketch the plane curve with the given vector equation. (b) Find...
 13.2.4: (a) Sketch the plane curve with the given vector equation. (b) Find...
 13.2.5: (a) Sketch the plane curve with the given vector equation. (b) Find...
 13.2.6: (a) Sketch the plane curve with the given vector equation. (b) Find...
 13.2.7: (a) Sketch the plane curve with the given vector equation. (b) Find...
 13.2.8: (a) Sketch the plane curve with the given vector equation. (b) Find...
 13.2.9: Find the derivative of the vector function.
 13.2.10: Find the derivative of the vector function.
 13.2.11: Find the derivative of the vector function.
 13.2.12: Find the derivative of the vector function.
 13.2.13: Find the derivative of the vector function.
 13.2.14: Find the derivative of the vector function.
 13.2.15: Find the derivative of the vector function.
 13.2.16: Find the derivative of the vector function.
 13.2.17: Find the unit tangent vector at the point with the given value of t...
 13.2.18: Find the unit tangent vector at the point with the given value of t...
 13.2.19: Find the unit tangent vector at the point with the given value of t...
 13.2.20: Find the unit tangent vector at the point with the given value of t...
 13.2.21: rt t, t rt, T1, rt, rt rt. 2 , t 3
 13.2.22: rt e T0 r0 rt rt. 2t , e2t , te
 13.2.23: Find parametric equations for the tangent line to the curve with th...
 13.2.24: Find parametric equations for the tangent line to the curve with th...
 13.2.25: Find parametric equations for the tangent line to the curve with th...
 13.2.26: Find parametric equations for the tangent line to the curve with th...
 13.2.27: Find parametric equations for the tangent line to the curve with th...
 13.2.28: Find parametric equations for the tangent line to the curve with th...
 13.2.29: Determine whether the curve is smooth.
 13.2.30: (a) Find the point of intersection of the tangent lines to the curv...
 13.2.31: The curves and intersect at the origin. Find their angle of interse...
 13.2.32: At what point do the curves and intersect? Find their angle of inte...
 13.2.33: Evaluate the integral.
 13.2.34: Evaluate the integral.
 13.2.35: Evaluate the integral.
 13.2.36: Evaluate the integral.
 13.2.37: Evaluate the integral.
 13.2.38: Evaluate the integral.
 13.2.39: Find if rt t r0 j 2 i 4t3 j t and .
 13.2.40: Find rt rt sin t i cos t j 2t k rt t r r0 i j 2 krt rt
 13.2.41: Prove Formula 1 of Theorem 3.
 13.2.42: Prove Formula 3 of Theorem 3.
 13.2.43: Prove Formula 5 of Theorem 3.
 13.2.44: Prove Formula 6 of Theorem 3.
 13.2.45: If and
 13.2.46: If and are the vector functions in Exercise 45, find
 13.2.47: Show that if is a vector function such that exists, then
 13.2.48: Find an expression for
 13.2.49: If , show that . [Hint: ]
 13.2.50: If a curve has the property that the position vector is always perp...
 13.2.51: If , show that ut rt rt r t ut rt rt
Solutions for Chapter 13.2: Derivatives and Integrals of Vector Functions
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 13.2: Derivatives and Integrals of Vector Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 13.2: Derivatives and Integrals of Vector Functions includes 51 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Calculus, was written by and is associated to the ISBN: 9780534393397. Since 51 problems in chapter 13.2: Derivatives and Integrals of Vector Functions have been answered, more than 43472 students have viewed full stepbystep solutions from this chapter.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Explanatory variable
A variable that affects a response variable.

Exponential function
A function of the form ƒ(x) = a ? bx,where ?0, b > 0 b ?1

Firstdegree equation in x , y, and z
An equation that can be written in the form.

Focal length of a parabola
The directed distance from the vertex to the focus.

Frequency (in statistics)
The number of individuals or observations with a certain characteristic.

Leaf
The final digit of a number in a stemplot.

Line of travel
The path along which an object travels

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Midpoint (on a number line)
For the line segment with endpoints a and b, a + b2

Multiplication principle of probability
If A and B are independent events, then P(A and B) = P(A) # P(B). If Adepends on B, then P(A and B) = P(AB) # P(B)

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Normal curve
The graph of ƒ(x) = ex2/2

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

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

symmetric about the xaxis
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

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k