 9.5.9.5.1: Fill in the blanks. If f and g are continuous functions of t on an ...
 9.5.9.5.2: Fill in the blanks. The _______ of a curve is the direction in whic...
 9.5.9.5.3: Fill in the blanks. The process of converting a set of parametric e...
 9.5.9.5.4: In Exercises 16, match the set of parametric equations with its gra...
 9.5.9.5.5: In Exercises 16, match the set of parametric equations with its gra...
 9.5.9.5.6: In Exercises 16, match the set of parametric equations with its gra...
 9.5.9.5.7: Consider the parametric equations and (a) Create a table of and val...
 9.5.9.5.8: Consider the parametric equations and (a) Create a table of and val...
 9.5.9.5.9: Library of Parent Functions In Exercises 9 and 10, determine the pl...
 9.5.9.5.10: Library of Parent Functions In Exercises 9 and 10, determine the pl...
 9.5.9.5.11: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.12: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.13: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.14: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.15: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.16: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.17: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.18: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.19: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.20: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.21: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.22: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.23: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.24: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.25: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.26: In Exercises 1126, sketch the curve represented by the parametric e...
 9.5.9.5.27: In Exercises 2732, use a graphing utility to graph the curve repres...
 9.5.9.5.28: In Exercises 2732, use a graphing utility to graph the curve repres...
 9.5.9.5.29: In Exercises 2732, use a graphing utility to graph the curve repres...
 9.5.9.5.30: In Exercises 2732, use a graphing utility to graph the curve repres...
 9.5.9.5.31: In Exercises 2732, use a graphing utility to graph the curve repres...
 9.5.9.5.32: In Exercises 2732, use a graphing utility to graph the curve repres...
 9.5.9.5.33: In Exercises 33 and 34, determine how the plane curves differ from ...
 9.5.9.5.34: In Exercises 33 and 34, determine how the plane curves differ from ...
 9.5.9.5.35: In Exercises 3538, eliminate the parameter and obtain the standard ...
 9.5.9.5.36: In Exercises 3538, eliminate the parameter and obtain the standard ...
 9.5.9.5.37: In Exercises 3538, eliminate the parameter and obtain the standard ...
 9.5.9.5.38: In Exercises 3538, eliminate the parameter and obtain the standard ...
 9.5.9.5.39: In Exercises 3942, use the results of Exercises 37 40 to find a set...
 9.5.9.5.40: In Exercises 3942, use the results of Exercises 37 40 to find a set...
 9.5.9.5.41: In Exercises 3942, use the results of Exercises 37 40 to find a set...
 9.5.9.5.42: In Exercises 3942, use the results of Exercises 37 40 to find a set...
 9.5.9.5.43: In Exercises 43 48, find two different sets of parametric equations...
 9.5.9.5.44: In Exercises 43 48, find two different sets of parametric equations...
 9.5.9.5.45: In Exercises 43 48, find two different sets of parametric equations...
 9.5.9.5.46: In Exercises 43 48, find two different sets of parametric equations...
 9.5.9.5.47: In Exercises 43 48, find two different sets of parametric equations...
 9.5.9.5.48: In Exercises 43 48, find two different sets of parametric equations...
 9.5.9.5.49: In Exercises 49 and 50, use a graphing utility to graph the curve r...
 9.5.9.5.50: In Exercises 49 and 50, use a graphing utility to graph the curve r...
 9.5.9.5.51: In Exercises 5154, match the parametric equations with the correct ...
 9.5.9.5.52: In Exercises 5154, match the parametric equations with the correct ...
 9.5.9.5.53: In Exercises 5154, match the parametric equations with the correct ...
 9.5.9.5.54: In Exercises 5154, match the parametric equations with the correct ...
 9.5.9.5.55: Projectile Motion In Exercises 5558, consider a projectile launched...
 9.5.9.5.56: Projectile Motion In Exercises 5558, consider a projectile launched...
 9.5.9.5.57: Projectile Motion In Exercises 5558, consider a projectile launched...
 9.5.9.5.58: Projectile Motion In Exercises 5558, consider a projectile launched...
 9.5.9.5.59: True or False? In Exercises 5962, determine whether the statement i...
 9.5.9.5.60: True or False? In Exercises 5962, determine whether the statement i...
 9.5.9.5.61: True or False? In Exercises 5962, determine whether the statement i...
 9.5.9.5.62: True or False? In Exercises 5962, determine whether the statement i...
 9.5.9.5.63: As increases, the ellipse given by the parametric equations and is ...
 9.5.9.5.64: Think About It The graph of the parametric equations and is shown b...
 9.5.9.5.65: In Exercises 6568, check for symmetry with respect to both axes and...
 9.5.9.5.66: In Exercises 6568, check for symmetry with respect to both axes and...
 9.5.9.5.67: In Exercises 6568, check for symmetry with respect to both axes and...
 9.5.9.5.68: In Exercises 6568, check for symmetry with respect to both axes and...
Solutions for Chapter 9.5: Parametric Equations
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 9.5: Parametric Equations
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Chapter 9.5: Parametric Equations includes 68 full stepbystep solutions. Since 68 problems in chapter 9.5: Parametric Equations have been answered, more than 103152 students have viewed full stepbystep solutions from this chapter.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Sum V + W of subs paces.
Space of all (v in V) + (w in W). Direct sum: V n W = to}.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B IIĀ·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.