 3.10.1E: Area Suppose that the radius r and area A = ?r2 of a circle are dif...
 3.10.2E: Surface area Suppose that the radius r and surface area S = 4?r2 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 x = y3 – y and dy/dt = 5, then what is dx/dt when y = 2?
 3.10.7E: If x2 + y2 = 25 and dx/dt = 2, then what is dy/dt when x = 3 and y...
 3.10.8E: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?
 3.10.9E: If and dy/dt = 3, find dL/dt when x = 5 and y = 12.
 3.10.10E: If r + s2 + v3 = 12, dr/dt = 4, and ds/dt = 3, find dv/dt when r =...
 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 ...
 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 50 m3/...
 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 perfect sphere ...
 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 y = x2 ...
 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...
Solutions for Chapter 3.10: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 3.10
Get Full SolutionsSince 44 problems in chapter 3.10 have been answered, more than 58525 students have viewed full stepbystep solutions from this chapter. 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. Chapter 3.10 includes 44 full stepbystep solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399.

Arccotangent function
See Inverse cotangent function.

Basic logistic function
The function ƒ(x) = 1 / 1 + ex

Constraints
See Linear programming problem.

Equation
A statement of equality between two expressions.

Imaginary axis
See Complex plane.

Intercept
Point where a curve crosses the x, y, or zaxis in a graph.

Inverse of a matrix
The inverse of a square matrix A, if it exists, is a matrix B, such that AB = BA = I , where I is an identity matrix.

Leaf
The final digit of a number in a stemplot.

Length of a vector
See Magnitude of a vector.

Multiplicative inverse of a real number
The reciprocal of b, or 1/b, b Z 0

Nappe
See Right circular cone.

Natural exponential function
The function ƒ1x2 = ex.

Parabola
The graph of a quadratic function, or the set of points in a plane that are equidistant from a fixed point (the focus) and a fixed line (the directrix).

Parallel lines
Two lines that are both vertical or have equal slopes.

Piecewisedefined function
A function whose domain is divided into several parts with a different function rule applied to each part, p. 104.

Projectile motion
The movement of an object that is subject only to the force of gravity

Relevant domain
The portion of the domain applicable to the situation being modeled.

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

Synthetic division
A procedure used to divide a polynomial by a linear factor, x  a

Unit vector in the direction of a vector
A unit vector that has the same direction as the given vector.