 10.2.1: Find dy/dx.
 10.2.2: Find dy/dx.
 10.2.3: Find an equation of the tangent to the curve at the point correspon...
 10.2.4: Find an equation of the tangent to the curve at the point correspon...
 10.2.5: Find an equation of the tangent to the curve at the point correspon...
 10.2.6: Find an equation of the tangent to the curve at the point correspon...
 10.2.7: Find an equation of the tangent to the curve at the given point by ...
 10.2.8: Find an equation of the tangent to the curve at the given point by ...
 10.2.9: Find an equation of the tangent(s) to the curve at the given point....
 10.2.10: Find an equation of the tangent(s) to the curve at the given point....
 10.2.11: Find and . For which values of is the curve concave upward?
 10.2.12: Find and . For which values of is the curve concave upward?
 10.2.13: Find and . For which values of is the curve concave upward?
 10.2.14: Find and . For which values of is the curve concave upward?
 10.2.15: Find and . For which values of is the curve concave upward?
 10.2.16: Find and . For which values of is the curve concave upward?
 10.2.17: Find the points on the curve where the tangent is horizontal or ver...
 10.2.18: Find the points on the curve where the tangent is horizontal or ver...
 10.2.19: Find the points on the curve where the tangent is horizontal or ver...
 10.2.20: Find the points on the curve where the tangent is horizontal or ver...
 10.2.21: Use a graph to estimate the coordinates of the rightmost point on t...
 10.2.22: Use a graph to estimate the coordinates of the lowest point and the...
 10.2.23: Graph the curve in a viewing rectangle that displays all the import...
 10.2.24: Graph the curve in a viewing rectangle that displays all the import...
 10.2.25: Show that the curve , has two tangents at and find their equations....
 10.2.26: Graph the curve , to discover where it crosses itself. Then find eq...
 10.2.27: (a) Find the slope of the tangent line to the trochoid , in terms o...
 10.2.28: (a) Find the slope of the tangent to the astroid , in terms of . (A...
 10.2.29: At what points on the curve , does the tangent line have slope ?
 10.2.30: Find equations of the tangents to the curve , that pass through the...
 10.2.31: Use the parametric equations of an ellipse, , , , to find the area ...
 10.2.32: Find the area enclosed by the curve , and the .
 10.2.33: Find the area enclosed by the and the curve , .
 10.2.34: Find the area of the region enclosed by the astroid , . (Astroids a...
 10.2.35: Find the area under one arch of the trochoid of Exercise 40 in Sect...
 10.2.36: Let be the region enclosed by the loop of the curve in Example 1. (...
 10.2.37: Set up an integral that represents the length of the curve. Then us...
 10.2.38: Set up an integral that represents the length of the curve. Then us...
 10.2.39: Set up an integral that represents the length of the curve. Then us...
 10.2.40: Set up an integral that represents the length of the curve. Then us...
 10.2.41: Find the exact length of the curve.
 10.2.42: Find the exact length of the curve.
 10.2.43: Find the exact length of the curve.
 10.2.44: Find the exact length of the curve.
 10.2.45: Graph the curve and find its length
 10.2.46: Graph the curve and find its length
 10.2.47: Graph the curve , and find its length correct to four decimal places.
 10.2.48: Find the length of the loop of the curve Use Simpsons Rule with to ...
 10.2.49: Use Simpsons Rule with to estimate the length of the curve
 10.2.50: In Exercise 43 in Section 10.1 you were asked to derive the paramet...
 10.2.51: Find the distance traveled by a particle with position as varies in...
 10.2.52: Find the distance traveled by a particle with position as varies in...
 10.2.53: Show that the total length of the ellipse , , , is
 10.2.54: Find the total length of the astroid , , where
 10.2.55: (a) Graph the epitrochoid with equations What parameter interval gi...
 10.2.56: A curve called Cornus spiral is defined by the parametric equations...
 10.2.57: Set up an integral that represents the area of the surface obtained...
 10.2.58: Set up an integral that represents the area of the surface obtained...
 10.2.59: Set up an integral that represents the area of the surface obtained...
 10.2.60: Set up an integral that represents the area of the surface obtained...
 10.2.61: Find the exact area of the surface obtained by rotating the given c...
 10.2.62: Find the exact area of the surface obtained by rotating the given c...
 10.2.63: Find the exact area of the surface obtained by rotating the given c...
 10.2.64: Graph the curve If this curve is rotated about the axis, find the ...
 10.2.65: Find the surface area generated by rotating the given curve about t...
 10.2.66: Find the surface area generated by rotating the given curve about t...
 10.2.67: If is continuous and for , show that the parametric curve , , , can...
 10.2.68: Use Formula 2 to derive Formula 7 from Formula 8.2.5 for the case i...
 10.2.69: The curvature at a point of a curve is defined as where is the angl...
 10.2.70: (a) Use the formula in Exercise 69(b) to find the curvature of the ...
 10.2.71: Use the formula in Exercise 69(a) to find the curvature of the cycl...
 10.2.72: (a) Show that the curvature at each point of a straight line is . (...
 10.2.73: A string is wound around a circle and then unwound while being held...
 10.2.74: A cow is tied to a silo with radius by a rope just long enough to r...
Solutions for Chapter 10.2: CALCULUS WITH PARAMETRIC CURVES
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 10.2: CALCULUS WITH PARAMETRIC CURVES
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 10.2: CALCULUS WITH PARAMETRIC CURVES includes 74 full stepbystep solutions. Since 74 problems in chapter 10.2: CALCULUS WITH PARAMETRIC CURVES have been answered, more than 21931 students have viewed full stepbystep solutions from this chapter. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

Circle graph
A circular graphical display of categorical data

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Determinant
A number that is associated with a square matrix

Factored form
The left side of u(v + w) = uv + uw.

First quartile
See Quartile.

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

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Linear regression
A procedure for finding the straight line that is the best fit for the data

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

Modulus
See Absolute value of a complex number.

Negative angle
Angle generated by clockwise rotation.

Parametric curve
The graph of parametric equations.

Partial fractions
The process of expanding a fraction into a sum of fractions. The sum is called the partial fraction decomposition of the original fraction.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Regression model
An equation found by regression and which can be used to predict unknown values.

Response variable
A variable that is affected by an explanatory variable.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Sum of a finite arithmetic series
Sn = na a1 + a2 2 b = n 2 32a1 + 1n  12d4,

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Zero vector
The vector <0,0> or <0,0,0>.