 3.10.1E: Area Suppose that the radius r and area of a circle are differentia...
 3.10.2E: Surface area Suppose that the radius r and surface area S = 4r2 of ...
 3.10.3E: Assume that y = 5x and dx/dt = 2. Find dy/dt.
 3.10.4E: Assume that 2x + 3y = 12 and dy/dt = 2. Find dx/dt.
 3.10.5E: If y = x2 and dx/dt = 3, then what is dy/dt when x = 1?
 3.10.6E: If and dy/dt = 5,then what is dx/dt when y = 2?
 3.10.7E: If and dx/dt = –2, then what is dy/dt when x = 3 and y = 4??
 3.10.8E: If then what is dx/dt when x = 2?
 3.10.9E: If find when
 3.10.10E: If , , and , find when r = 3 and s = 1.
 3.10.11E: If the original 24 m edge length x of a cube decreases at the rate ...
 3.10.12E: A cube’s surface area increases at the rate of 72 in2/sec.At what r...
 3.10.13E: Volume The radius r and height h of a right circular cylinder are r...
 3.10.14E: Volume The radius r and height h of a right circular cone are relat...
 3.10.15E: Changing voltage The voltage V (volts), current I (amperes), and re...
 3.10.16E: Electrical power The power P (watts) of an electric circuit is rela...
 3.10.17E: Distance Let x and y be differentiable functions of t and let be th...
 3.10.18E: Diagonals If x, y, and z are lengths of the edges of a rectangular ...
 3.10.19E: Area The area A of a triangle with sides of lengths a and b enclosi...
 3.10.20E: Heating a plate When a circular plate of metal is heated in an oven...
 3.10.21E: Changing dimensions in a rectangle The length l of a rectangle is d...
 3.10.22E: Changing dimensions in a rectangular box Suppose that the edge leng...
 3.10.23E: A sliding ladder A 13ft ladder is leaning against a house when its...
 3.10.24E: Commercial air traffic Two commercial airplanes are flying at an al...
 3.10.25E: Flying a kite A girl flies a kite at a height of 300 ft, the wind c...
 3.10.26E: Boring a cylinder The mechanics at Lincoln Automotive are reboring ...
 3.10.27E: A growing sand pile Sand falls from a conveyor belt at the rate of ...
 3.10.28E: A draining conical reservoir Water is flowing at the rate of from a...
 3.10.29E: A draining hemispherical reservoir Water is flowing at the rate of ...
 3.10.30E: A growing raindrop Suppose that a drop of mist is a perfectsphere a...
 3.10.31E: The radius of an inflating balloon A spherical balloon is inflated ...
 3.10.32E: Hauling in a dinghy A dinghy is pulled toward a dock by a rope from...
 3.10.33E: A balloon and a bicycle A balloon is rising vertically above a leve...
 3.10.34E: Making coffee Coffee is draining from a conical filter into a cylin...
 3.10.35E: Cardiac output In the late 1860s, Adolf Fick, a professor of physio...
 3.10.36E: Moving along a parabola A particle moves along the parabola in the ...
 3.10.37E: Motion in the plane The coordinates of a particle in the metric xy...
 3.10.38E: Videotaping a moving car You are videotaping a race from a stand 13...
 3.10.39E: A moving shadow A light shines from the top of a pole 50 ft high. A...
 3.10.40E: A building’s shadow On a morning of a day when the sun will pass di...
 3.10.41E: A melting ice layer A spherical iron ball 8 in. in diameter is coat...
 3.10.42E: Highway patrol A highway patrol plane flies 3 mi above a level, str...
 3.10.43E: Baseball players A baseball diamond is a square 90 ft on a side. A ...
 3.10.44E: Ships Two ships are steaming straight away from a point O along rou...
 3.10.45E: Clock's moving hands At what rate is the angle between a clock's mi...
 3.10.46E: Oil spill An explosion at an oil rig located in gulf waters causes ...
Solutions for Chapter 3.10: Thomas' Calculus: Early Transcendentals 13th Edition
Full solutions for Thomas' Calculus: Early Transcendentals  13th Edition
ISBN: 9780321884077
Solutions for Chapter 3.10
Get Full SolutionsSince 46 problems in chapter 3.10 have been answered, more than 87537 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13. Thomas' Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321884077. Chapter 3.10 includes 46 full stepbystep solutions.

Characteristic polynomial of a square matrix A
det(xIn  A), where A is an n x n matrix

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

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

Imaginary axis
See Complex plane.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

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

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Logarithmic function with base b
The inverse of the exponential function y = bx, denoted by y = logb x

Measure of spread
A measure that tells how widely distributed data are.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Positive linear correlation
See Linear correlation.

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

Secant line of ƒ
A line joining two points of the graph of ƒ.

Sine
The function y = sin x.

Square matrix
A matrix whose number of rows equals the number of columns.

Symmetric matrix
A matrix A = [aij] with the property aij = aji for all i and j

Variable
A letter that represents an unspecified number.

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