 3. PE.13PE: Find the derivatives of the functions in Exercises 1– 64.s = cos4 (...
 3. PE.27PE: Find the derivatives of the functions in Exercises 1– 64.y = x2 sin...
 3. PE.41PE: Find the derivatives of the functions in Exercises 1– 64.y = 10e x/5
 3. PE.55PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.69PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.83PE: Find d2y/dx2 by implicit differentiation:
 3. PE.97PE: a. Graph the function b. Is ƒ continuous at x = 1?c. Is ƒ different...
 3. PE.7PE: Find the derivatives of the functions in Exercises 1– 64.y = (?2 + ...
 3. PE.111PE: In Exercises 111–116, find equations for the lines that are tangent...
 3. PE.21PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.125PE: Find the limits in Exercises 125–132.
 3. PE.35PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.49PE: Find the derivatives of the functions in Exercises 1– 64.y = 8t
 3. PE.63PE: Find the derivatives of the functions in Exercises 1– 64.y = csc1 ...
 3. PE.139PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3. PE.77PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.153PE: Find the linearizations of Graph the curves and linearizations toge...
 3. PE.105PE: Normals parallel to a line Find the points on the curve where the n...
 3. PE.91PE: If find the value of d2y/dx2 at the point (0, 1).
 3. PE.147PE: Speed of moving particle The coordinates of a particle moving in th...
 3. PE.133PE: Show how to extend the functions in Exercises 133 and 134 to be con...
 3. PE.119PE: Each of the figures in Exercises 119 and 120 shows two graphs, the ...
 3. PE.10PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.24PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.38PE: Find the derivatives of the functions in Exercises 1– 64.y = 20(3x ...
 3. PE.12PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.52PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.66PE: In Exercises 65–78, find dy/dx by implicit differentiation.x2 + xy ...
 3. PE.26PE: Find the derivatives of the functions in Exercises 1– 64.y = x2 cot 5x
 3. PE.80PE: In Exercises 79 and 80, find dp/dq.
 3. PE.94PE: Find the derivative using the definition.
 3. PE.40PE: Find the derivatives of the functions in Exercises 1– 64.y = (3 + c...
 3. PE.108PE: Slope of tangent Show that the tangent to the curve y = x3 at any p...
 3. PE.122PE: Repeat Exercise 121, supposing that the graph starts at (1, 0) ins...
 3. PE.54PE: Find the derivatives of the functions in Exercises 1– 64.y = 2(ln x...
 3. PE.136PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3. PE.150PE: Rotating spool As television cable is pulled from a large spool to ...
 3. PE.68PE: In Exercises 65–78, find dy/dx by implicit differentiation.5x4/5 + ...
 3. PE.82PE: In Exercises 81 and 82, find dr/ds.
 3. PE.96PE: a. Graph the function b. Is ƒ continuous at x = 0?c. Is ƒ different...
 3. PE.110PE: Normal to a circle Show that the normal line at any point of the ci...
 3. PE.124PE: Exercises 123 and 124 are about the accompanying graphs. The graphs...
 3. PE.138PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3. PE.152PE: Points moving on coordinate axes Points A and B move along the x a...
 3. PE.3PE: Find the derivatives of the functions in Exercises 1– 64.y = x3 – 3...
 3. PE.17PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.31PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.45PE: Find the derivatives of the functions in Exercises 1– 64.y = ln (si...
 3. PE.59PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.73PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.87PE: Find the value of dy/dt at t = 0 if and
 3. PE.101PE: Horizontal tangents Find the points on the curve y = 2x3  3x2  12...
 3. PE.115PE: In Exercises 111–116, find equations for the lines that are tangent...
 3. PE.129PE: Find the limits in Exercises 125–132.
 3. PE.143PE: Circle’s changing area The radius of a circle is changing at the ra...
 3. PE.157PE: Surface area of a cone Write a formula that estimates the change th...
 3. PE.8PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.22PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.36PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.50PE: Find the derivatives of the functions in Exercises 1– 64.y = 92t
 3. PE.64PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.78PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.92PE: If find d2y/dx2 at the point (8, 8).
 3. PE.106PE: Tangent and normal lines Find equations for the tangent and normal ...
 3. PE.120PE: Each of the figures in Exercises 119 and 120 shows two graphs, the ...
 3. PE.134PE: Show how to extend the functions in Exercises 133 and 134 to be con...
 3. PE.148PE: Motion of a particle A particle moves along the curve y = x3/2 in t...
 3. PE.11PE: Find the derivatives of the functions in Exercises 1– 64.y = 2 tan2...
 3. PE.25PE: Find the derivatives of the functions in Exercises 1– 64.y = 5 cot x2
 3. PE.53PE: Find the derivatives of the functions in Exercises 1– 64.y = (x + 2...
 3. PE.39PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.67PE: In Exercises 65–78, find dy/dx by implicit differentiation.x3 + 4xy...
 3. PE.81PE: In Exercises 81 and 82, find dr/ds.
 3. PE.95PE: a. Graph the function b. Is ƒ continuous at x = 0?c. Is ƒ different...
 3. PE.123PE: Exercises 123 and 124 are about the accompanying graphs. The graphs...
 3. PE.109PE: Tangent curve For what value of c is the curve y = c/(x + 1) tangen...
 3. PE.137PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3. PE.151PE: Moving searchlight beam The figure shows a boat 1 km offshore, swee...
 3. PE.6PE: Find the derivatives of the functions in Exercises 1– 64.y = (2x – ...
 3. PE.20PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.34PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.48PE: Find the derivatives of the functions in Exercises 1– 64.y = log5 (...
 3. PE.62PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.76PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.9PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.23PE: Find the derivatives of the functions in Exercises 1– 64.y = x1/2 ...
 3. PE.90PE: Find the value of dr/dt at t = 0 if and
 3. PE.37PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.51PE: Find the derivatives of the functions in Exercises 1– 64.y = 5x3.6
 3. PE.65PE: In Exercises 65–78, find dy/dx by implicit differentiation.xy + 2x ...
 3. PE.104PE: Intersecting tangents Show that the tangents to the curve intersect...
 3. PE.79PE: In Exercises 79 and 80, find dp/dq.
 3. PE.93PE: In Exercises 93 and 94, find the derivative using the definition.
 3. PE.107PE: Tangent parabola The parabola y = x2 + C is to be tangent to the li...
 3. PE.118PE: The graph shown suggests that the curve might have horizontal tange...
 3. PE.121PE: Use the following information to graph the function y = f(x) for i)...
 3. PE.135PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3. PE.132PE: Find the limits in Exercises 125–132.
 3. PE.149PE: Draining a tank Water drains from the conical tank shown in the acc...
 3. PE.146PE: Impedance in a series circuit The impedance Z (ohms) in a series ci...
 3. PE.160PE: Finding height To find the height of a lamppost (see accompanying f...
 3. PE.28PE: Find the derivatives of the functions in Exercises 1– 64.y = x2 si...
 3. PE.14PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.42PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.56PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.98PE: For what value or values of the constant m, if any, is a. continuou...
 3. PE.70PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.84PE: a. By differentiating implicitly, show that dy/dx = x/y.b. Then sho...
 3. PE.112PE: In Exercises 111–116, find equations for the lines that are tangent...
 3. PE.140PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3. PE.126PE: Find the limits in Exercises 125–132.
 3. PE.154PE: We can obtain a useful linear approximation of the function f(x) = ...
 3. PE.4PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.18PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.32PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.46PE: Find the derivatives of the functions in Exercises 1– 64.y = ln (se...
 3. PE.60PE: Find the derivatives of the functions in Exercises 1– 64.y = (1 + t...
 3. PE.74PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.88PE: Find the value of ds/du at u = 2 if and t = (u2 + 2u)1/3 .
 3. PE.102PE: Tangent intercepts Find the x and yintercepts of the line that is...
 3. PE.116PE: In Exercises 111–116, find equations for the lines that are tangent...
 3. PE.130PE: Find the limits in Exercises 125–132.
 3. PE.144PE: Cube’s changing edges The volume of a cube is increasing at the rat...
 3. PE.158PE: Controlling errora. How accurately should you measure the edge of a...
 3. PE.1PE: Find the derivatives of the functions in Exercises 1– 64.y = x5  0...
 3. PE.15PE: Find the derivatives of the functions in Exercises 1– 64.s = (sec t...
 3. PE.29PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.43PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.113PE: In Exercises 111–116, find equations for the lines that are tangent...
 3. PE.71PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.85PE: Suppose that functions ƒ(x) and g(x) and their first derivatives ha...
 3. PE.99PE: Tangents with specified slope Are there any points on the curve whe...
 3. PE.57PE: Find the derivatives of the functions in Exercises 1– 64.y = ln cos...
 3. PE.155PE: Find the linearization of at x = 0.
 3. PE.141PE: Right circular cylinder The total surface area S of a right circula...
 3. PE.127PE: Find the limits in Exercises 125–132.
 3. PE.5PE: Find the derivatives of the functions in Exercises 1– 64.y = (x + 1...
 3. PE.19PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.33PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.47PE: Find the derivatives of the functions in Exercises 1– 64.y = log2 (...
 3. PE.61PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.75PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.89PE: Find the value of dw/ds at s = 0 if and
 3. PE.103PE: Tangents perpendicular or parallel to lines Find the points on the ...
 3. PE.117PE: Find the slope of the curve at the points (1, 1) and (1, 1).
 3. PE.131PE: Find the limits in Exercises 125–132.
 3. PE.145PE: Resistors connected in parallel If two resistors of R1 and R2 ohms ...
 3. PE.159PE: Compounding error The circumference of the equator of a sphere is m...
 3. PE.2PE: Find the derivatives of the functions in Exercises 1– 64.y = 3  0....
 3. PE.16PE: Find the derivatives of the functions in Exercises 1– 64.s = csc5 (...
 3. PE.44PE: Find the derivatives of the functions in Exercises 1– 64.y = x2e2/x
 3. PE.30PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.72PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3. PE.58PE: Find the derivatives of the functions in Exercises 1– 64.
 3. PE.86PE: Suppose that the function ƒ(x) and its first derivative have the fo...
 3. PE.100PE: Tangents with specified slope Are there any points on the curve whe...
 3. PE.114PE: In Exercises 111–116, find equations for the lines that are tangent...
 3. PE.142PE: Right circular cone The lateral surface area S of a right circular ...
 3. PE.128PE: Find the limits in Exercises 125–132.
 3. PE.156PE: Find the linearization of at x = 0.
Solutions for Chapter 3. PE: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 3. PE
Get Full SolutionsChapter 3. PE includes 160 full stepbystep solutions. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Since 160 problems in chapter 3. PE have been answered, more than 62171 students have viewed full stepbystep solutions from this chapter. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399.

Completing the square
A method of adding a constant to an expression in order to form a perfect square

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Equation
A statement of equality between two expressions.

Equilibrium price
See Equilibrium point.

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

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

Gaussian elimination
A method of solving a system of n linear equations in n unknowns.

Histogram
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.

Interval notation
Notation used to specify intervals, pp. 4, 5.

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

Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.

Quotient identities
tan ?= sin ?cos ?and cot ?= cos ? sin ?

Random behavior
Behavior that is determined only by the laws of probability.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Terminal side of an angle
See Angle.

Translation
See Horizontal translation, Vertical translation.

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.

Weighted mean
A mean calculated in such a way that some elements of the data set have higher weights (that is, are counted more strongly in determining the mean) than others.

Xmax
The xvalue of the right side of the viewing window,.

Zero factorial
See n factorial.