 13.PE.1PE: In Exercises 1–4, find the domain and range of the given function a...
 13.PE.2PE: find the domain and range of the given function and identify its le...
 13.PE.3PE: find the domain and range of the given function and identify its le...
 13.PE.4PE: find the domain and range of the given function and identify its le...
 13.PE.5PE: find the domain and range of the given function and identify its le...
 13.PE.6PE: find the domain and range of the given function and identify its le...
 13.PE.7PE: find the domain and range of the given function and identify its le...
 13.PE.9PE: Find the limits.
 13.PE.8PE: find the domain and range of the given function and identify its le...
 13.PE.10PE: Find the limits.
 13.PE.11PE: Find the limits.
 13.PE.12PE: Find the limits.
 13.PE.13PE: Find the limits.
 13.PE.14PE: Find the limits.
 13.PE.15PE: By considering different paths of approach, show that the limits in...
 13.PE.16PE: By considering different paths of approach, show that the limits in...
 13.PE.17PE: Continuous extension Let for Is it possible to define ƒ(0, 0) in a ...
 13.PE.18PE: Continuous extension Let Is ƒ continuous at the origin? Why?
 13.PE.19PE: find the partial derivative of the function with respect to each va...
 13.PE.20PE: find the partial derivative of the function with respect to each va...
 13.PE.21PE: find the partial derivative of the function with respect to each va...
 13.PE.22PE: find the partial derivative of the function with respect to each va...
 13.PE.23PE: find the partial derivative of the function with respect to each va...
 13.PE.24PE: find the partial derivative of the function with respect to each va...
 13.PE.25PE: Find the secondorder partial derivatives of the functions
 13.PE.26PE: Find the secondorder partial derivatives of the functions
 13.PE.27PE: Find the secondorder partial derivatives of the functions
 13.PE.28PE: Find the secondorder partial derivatives of the functions
 13.PE.29PE: Find
 13.PE.30PE:
 13.PE.31PE:
 13.PE.32PE:
 13.PE.33PE: Find the value of the derivative of withrespect to t on the curve
 13.PE.34PE: Show that if w=f(s) is any differentiable function of s and if s=y+...
 13.PE.35PE: Assuming that the equations in Exercises 35 and 36 define y as a di...
 13.PE.36PE: Assuming that the equations in Exercises 35 and 36 define y as a di...
 13.PE.37PE: In Exercises 37–40, find the directions in which ƒ increases and de...
 13.PE.38PE: In Exercises 37–40, find the directions in which ƒ increases and de...
 13.PE.39PE: In Exercises 37–40, find the directions in which ƒ increases and de...
 13.PE.40PE: In Exercises 37–40, find the directions in which ƒ increases and de...
 13.PE.41PE: Derivative in velocity direction Find the derivative of f(x,y,z)=xy...
 13.PE.42PE: Maximum directional derivative What is the largest value that the d...
 13.PE.43PE: Directional derivatives with given values At the point (1, 2), the ...
 13.PE.44PE: Which of the following statements are true if ƒ(x, y) is differenti...
 13.PE.45PE: In Exercises 45 and 46, sketch the surface together with at the giv...
 13.PE.46PE: In Exercises 45 and 46, sketch the surface at the given points.
 13.PE.47PE: find an equation for the plane tangent to the level surface f(x,y,z...
 13.PE.48PE: find an equation for the plane tangent to the level surface f(x,y,z...
 13.PE.49PE: find an equation for the plane tangent to the surface z=f(x,y,z) at...
 13.PE.50PE: find an equation for the plane tangent to the surface z=f(x,y,z) at...
 13.PE.51PE: find equations for the lines that are tangent and normal to the lev...
 13.PE.52PE: find equations for the lines that are tangent and normal to the lev...
 13.PE.53PE: find parametric equations for the line that is tangent to the curve...
 13.PE.54PE: find parametric equations for the line that is tangent to the curve...
 13.PE.55PE: find parametric equations for the line that is tangent to the curve...
 13.PE.56PE: find parametric equations for the line that is tangent to the curve...
 13.PE.57PE: Find the linearizations of the functions in Exercises 57 and 58 at ...
 13.PE.58PE: Find the linearizations of the functions in Exercises 57 and 58 at ...
 13.PE.59PE: Measuring the volume of a pipeline You plan to calculate the volume...
 13.PE.60PE: Sensitivity to change Is more sensitive to changes in x or to chang...
 13.PE.61PE: Change in an electrical circuit Suppose that the current I (amperes...
 13.PE.62PE: Maximum error in estimating the area of an ellipse If a=10 cm And b...
 13.PE.63PE: Error in estimating a product Let y=uv and z=u+v, where u and are p...
 13.PE.64PE: Cardiac index To make different people comparable in studies of car...
 13.PE.65PE: Test the functions in Exercises 65–70 for local maxima and minima a...
 13.PE.66PE: Test the functions in Exercises 65–70 for local maxima and minima a...
 13.PE.67PE: Test the functions in Exercises 65–70 for local maxima and minima a...
 13.PE.68PE: Test the functions in Exercises 65–70 for local maxima and minima a...
 13.PE.69PE: Test the functions in Exercises 65–70 for local maxima and minima a...
 13.PE.70PE: Test the functions in Exercises 65–70 for local maxima and minima a...
 13.PE.71PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.72PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.73PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.74PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.75PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.76PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.77PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.78PE: find the absolute maximum and minimum values of ƒ on the region R.
 13.PE.79PE: Extrema on a circle Find the extreme values of f(x,y)=
 13.PE.80PE: Extrema on a circle Find the extreme values of f(x,y)=xy on the circle
 13.PE.81PE:
 13.PE.82PE:
 13.PE.83PE: Extrema on a sphere Find the extreme values of f(x,y,z)= xy+z on t...
 13.PE.84PE: Minimum distance to origin Find the points on the surface x2zy=4 c...
 13.PE.85PE: Minimizing cost of a box A closed rectangular box is to have volume...
 13.PE.86PE: Least volume Find the plane that passes through the point (2, 1, 2)...
 13.PE.87PE: Extrema on curve of intersecting surfaces Find the extreme values o...
 13.PE.88PE: Minimum distance to origin on curve of intersecting plane and cone ...
 13.PE.89PE:
 13.PE.90PE:
 13.PE.91PE:
 13.PE.92PE: Using the Chain Rule
 13.PE.93PE: Angle between vectors The equations as differentiable functions of ...
 13.PE.94PE: Polar coordinates and second derivatives Introducing polar coordina...
 13.PE.95PE: Normal line parallel to a plane Find the points on the surface wher...
 13.PE.96PE: Tangent plane parallel to xy plane Find the points on the surface ...
 13.PE.97PE: When gradient is parallel to position vector Suppose that is always...
 13.PE.98PE: Onesided directional derivative in all directions, but no gradient...
 13.PE.99PE: Normal line through origin Show that the line normal to the surface...
 13.PE.100PE: Tangent plane and normal linea. Sketch the surface b. Find a vector...
Solutions for Chapter 13.PE: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 13.PE
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399. Chapter 13.PE includes 100 full stepbystep solutions. Since 100 problems in chapter 13.PE have been answered, more than 55334 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2.

Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

Annual percentage rate (APR)
The annual interest rate

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Compound interest
Interest that becomes part of the investment

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Feasible points
Points that satisfy the constraints in a linear programming problem.

Finite series
Sum of a finite number of terms.

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

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

Interval
Connected subset of the real number line with at least two points, p. 4.

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Positive angle
Angle generated by a counterclockwise rotation.

Relation
A set of ordered pairs of real numbers.

Root of a number
See Principal nth root.

Solve an equation or inequality
To find all solutions of the equation or inequality

Symmetric about the origin
A graph in which (x, y) is on the the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ? + ?) is on the graph whenever (r, ?) is

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

Terminal side of an angle
See Angle.