 3.PE.1PE: Find the derivatives of the functions in Exercises 1– 64. y = x5  ...
 3.PE.2PE: Find the derivatives of the functions in Exercises 1– 64. y = 3  0...
 3.PE.3PE: Find the derivatives of the functions in Exercises 1– 64. y = x3 – ...
 3.PE.4PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.5PE: Find the derivatives of the functions in Exercises 1– 64. y = (x + ...
 3.PE.6PE: Find the derivatives of the functions in Exercises 1– 64. y = (2x –...
 3.PE.8PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.9PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.10PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.11PE: Find the derivatives of the functions in Exercises 1– 64. y = 2 tan...
 3.PE.12PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.13PE: Find the derivatives of the functions in Exercises 1– 64. s = cos4 ...
 3.PE.14PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.15PE: Find the derivatives of the functions in Exercises 1– 64. s = (sec ...
 3.PE.16PE: Find the derivatives of the functions in Exercises 1– 64. s = csc5 ...
 3.PE.17PE: 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.19PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.20PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.21PE: 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.23PE: Find the derivatives of the functions in Exercises 1– 64. y = x1/2...
 3.PE.24PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.25PE: Find the derivatives of the functions in Exercises 1– 64. y = 5 cot x2
 3.PE.26PE: Find the derivatives of the functions in Exercises 1– 64. y = x2 co...
 3.PE.27PE: Find the derivatives of the functions in Exercises 1– 64. 2? 2? 2? ...
 3.PE.28PE: Find the derivatives of the functions in Exercises 1– 64. y = x2 s...
 3.PE.29PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.30PE: 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.32PE: 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.34PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.35PE: 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.37PE: 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.39PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.40PE: Find the derivatives of the functions in Exercises 1– 64. y = (3 + ...
 3.PE.41PE: Find the derivatives of the functions in Exercises 1– 64. y ? = 10?...
 3.PE.42PE: 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.44PE: Find the derivatives of the functions in Exercises 1– 64. y = x2e2/x
 3.PE.45PE: Find the derivatives of the functions in Exercises 1– 64. y = ln (s...
 3.PE.46PE: Find the derivatives of the functions in Exercises 1– 64. y = ln (s...
 3.PE.47PE: Find the derivatives of the functions in Exercises 1– 64. y = log2 ...
 3.PE.48PE: Find the derivatives of the functions in Exercises 1– 64. y = log5 ...
 3.PE.49PE: Find the derivatives of the functions in Exercises 1– 64. y = 8t
 3.PE.50PE: Find the derivatives of the functions in Exercises 1– 64. y = 92t
 3.PE.51PE: Find the derivatives of the functions in Exercises 1– 64. y = 5x3.6
 3.PE.52PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.53PE: Find the derivatives of the functions in Exercises 1– 64. y = (x + ...
 3.PE.54PE: Find the derivatives of the functions in Exercises 1– 64. y = 2(ln ...
 3.PE.55PE: 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.57PE: Find the derivatives of the functions in Exercises 1– 64. y = ln co...
 3.PE.58PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.59PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.60PE: Find the derivatives of the functions in Exercises 1– 64. y = (1 + ...
 3.PE.61PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.62PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.63PE: Find the derivatives of the functions in Exercises 1– 64. y = csc1...
 3.PE.64PE: Find the derivatives of the functions in Exercises 1– 64.
 3.PE.65PE: In Exercises 65–78, find dy/dx by implicit differentiation. xy + 2x...
 3.PE.66PE: In Exercises 65–78, find dy/dx by implicit differentiation. x2 + xy...
 3.PE.67PE: In Exercises 65–78, find dy/dx by implicit differentiation. x3 + 4x...
 3.PE.68PE: In Exercises 65–78, find dy/dx by implicit differentiation. 5x4/5 +...
 3.PE.69PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.70PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.71PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.72PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.73PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.74PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.75PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.76PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.77PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.78PE: In Exercises 65–78, find dy/dx by implicit differentiation.
 3.PE.79PE: In Exercises 79 and 80, find dp/dq.
 3.PE.80PE: In Exercises 79 and 80, find dp/dq.
 3.PE.81PE: In Exercises 81 and 82, find dr/ds.
 3.PE.82PE: In Exercises 81 and 82, find dr/ds.
 3.PE.83PE: Find d2y/dx2 by implicit differentiation:
 3.PE.84PE: a. By differentiating implicitly, show that dy/dx = x/y. b. Then sh...
 3.PE.85PE: Suppose that functions ƒ(x) and g(x) and their first derivatives ha...
 3.PE.86PE: Suppose that the function ƒ(x) and its first derivative have the fo...
 3.PE.87PE: Find the value of dy/dt at t = 0 if and
 3.PE.88PE: Find the value of ds/du at u = 2 if and t = (u2 + 2u)1/3 .
 3.PE.89PE: Find the value of dw/ds at s = 0 if and Find the value of dw/ds at ...
 3.PE.90PE: Find the value of dr/dt at t = 0 if and
 3.PE.91PE: If find the value of d2y/dx2 at the point (0, 1).
 3.PE.92PE: If find d2y/dx2 at the point (8, 8).
 3.PE.93PE: In Exercises 93 and 94, find the derivative using the definition.
 3.PE.94PE: 94PE
 3.PE.95PE: a. Graph the function b. Is ƒ continuous at x = 0? c. Is ƒ differen...
 3.PE.96PE: a. Graph the function b. Is ƒ continuous at x = 0? c. Is ƒ differen...
 3.PE.97PE: a. Graph the function b. Is ƒ continuous at x = 1? c. Is ƒ differen...
 3.PE.98PE: For what value or values of the constant m, if any, is a. continuou...
 3.PE.99PE: Tangents with specified slope Are there any points on the curve whe...
 3.PE.100PE: Tangents with specified slope Are there any points on the curve whe...
 3.PE.101PE: Horizontal tangents Find the points on the curve y = 2x3  3x2  12...
 3.PE.110PE: Normal to a circle Show that the normal line at any point of the ci...
 3.PE.102PE: Tangent intercepts Find the x and yintercepts of the line that is...
 3.PE.103PE: Tangents perpendicular or parallel to lines Find the points on the ...
 3.PE.104PE: Intersecting tangents Show that the tangents to the curve intersect...
 3.PE.105PE: Normals parallel to a line Find the points on the curve where the n...
 3.PE.106PE: Tangent and normal lines Find equations for the tangent and normal ...
 3.PE.107PE: Tangent parabola The parabola y = x2 + C is to be tangent to the li...
 3.PE.108PE: Slope of tangent Show that the tangent to the curve y = x3 at any p...
 3.PE.109PE: Tangent curve For what value of c is the curve y = c/(x + 1) tangen...
 3.PE.111PE: In Exercises 111–116, find equations for the lines that are tangent...
 3.PE.112PE: In Exercises 111–116, find equations for the lines that are tangent...
 3.PE.113PE: In Exercises 111–116, find equations for the lines that are tangent...
 3.PE.114PE: In Exercises 111–116, find equations for the lines that are tangent...
 3.PE.115PE: In Exercises 111–116, find equations for the lines that are tangent...
 3.PE.116PE: In Exercises 111–116, find equations for the lines that are tangent...
 3.PE.117PE: Find the slope of the curve at the points (1, 1) and (1, 1).
 3.PE.118PE: The graph shown suggests that the curve might have horizontal tange...
 3.PE.119PE: Each of the figures in Exercises 119 and 120 shows two graphs, the ...
 3.PE.120PE: Each of the figures in Exercises 119 and 120 shows two graphs, the ...
 3.PE.121PE: Use the following information to graph the function y = f(x) for i)...
 3.PE.122PE: Repeat Exercise 121, supposing that the graph starts at (1, 0) ins...
 3.PE.123PE: Exercises 123 and 124 are about the accompanying graphs. The graphs...
 3.PE.124PE: Exercises 123 and 124 are about the accompanying graphs. The graphs...
 3.PE.125PE: Find the limits in Exercises 125–132.
 3.PE.126PE: Find the limits in Exercises 125–132.
 3.PE.127PE: Find the limits in Exercises 125–132.
 3.PE.128PE: Find the limits in Exercises 125–132.
 3.PE.129PE: Find the limits in Exercises 125–132.
 3.PE.130PE: Find the limits in Exercises 125–132.
 3.PE.131PE: Find the limits in Exercises 125–132.
 3.PE.132PE: Find the limits in Exercises 125–132.
 3.PE.133PE: Show how to extend the functions in Exercises 133 and 134 to be con...
 3.PE.134PE: Show how to extend the functions in Exercises 133 and 134 to be con...
 3.PE.135PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3.PE.136PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3.PE.137PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3.PE.138PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3.PE.139PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3.PE.140PE: In Exercises 135–140, use logarithmic differentiation to find the d...
 3.PE.141PE: Right circular cylinder The total surface area S of a right circula...
 3.PE.142PE: Right circular cone The lateral surface area S of a right circular ...
 3.PE.143PE: Circle’s changing area The radius of a circle is changing at the ra...
 3.PE.144PE: Cube’s changing edges The volume of a cube is increasing at the rat...
 3.PE.145PE: Resistors connected in parallel If two resistors of R1 and R2 ohms ...
 3.PE.146PE: Impedance in a series circuit The impedance Z (ohms) in a series ci...
 3.PE.147PE: Speed of moving particle The coordinates of a particle moving in th...
 3.PE.148PE: Motion of a particle A particle moves along the curve y = x3/2 in t...
 3.PE.149PE: Draining a tank Water drains from the conical tank shown in the acc...
 3.PE.150PE: Rotating spool As television cable is pulled from a large spool to ...
 3.PE.151PE: Moving searchlight beam The figure shows a boat 1 km offshore, swee...
 3.PE.152PE: Points moving on coordinate axes Points A and B move along the x a...
 3.PE.153PE: Find the linearizations of Graph the curves and linearizations toge...
 3.PE.154PE: We can obtain a useful linear approximation of the function f(x) = ...
 3.PE.155PE: Find the linearization of at x = 0.
 3.PE.156PE: Find the linearization of at x = 0.
 3.PE.157PE: Surface area of a cone Write a formula that estimates the change th...
 3.PE.158PE: Controlling error a. How accurately should you measure the edge of ...
 3.PE.159PE: Compounding error The circumference of the equator of a sphere is m...
 3.PE.160PE: Finding height To find the height of a lamppost (see accompanying f...
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 159 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. Since 159 problems in chapter 3.PE have been answered, more than 61753 students have viewed full stepbystep solutions from this chapter. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Closed interval
An interval that includes its endpoints

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Exponential regression
A procedure for fitting an exponential function to a set of data.

Fibonacci numbers
The terms of the Fibonacci sequence.

Frequency table (in statistics)
A table showing frequencies.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Identity function
The function ƒ(x) = x.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Infinite limit
A special case of a limit that does not exist.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

LRAM
A Riemann sum approximation of the area under a curve ƒ(x) from x = a to x = b using x1 as the lefthand endpoint of each subinterval

Minute
Angle measure equal to 1/60 of a degree.

Monomial function
A polynomial with exactly one term.

Pascal’s triangle
A number pattern in which row n (beginning with n = 02) consists of the coefficients of the expanded form of (a+b)n.

Vertices of a hyperbola
The points where a hyperbola intersects the line containing its foci.

Xscl
The scale of the tick marks on the xaxis in a viewing window.

Ymin
The yvalue of the bottom of the viewing window.

zcoordinate
The directed distance from the xyplane to a point in space, or the third number in an ordered triple.