 14.2.1: Suppose that . What can you say about the value of ? What if is con...
 14.2.2: Explain why each function is continuous or discontinuous. (a) The o...
 14.2.3: Use a table of numerical values of for near the origin to make a co...
 14.2.4: Use a table of numerical values of for near the origin to make a co...
 14.2.5: Find the limit, if it exists, or show that the limit does not exist.
 14.2.6: Find the limit, if it exists, or show that the limit does not exist.
 14.2.7: Find the limit, if it exists, or show that the limit does not exist.
 14.2.8: Find the limit, if it exists, or show that the limit does not exist.
 14.2.9: Find the limit, if it exists, or show that the limit does not exist.
 14.2.10: Find the limit, if it exists, or show that the limit does not exist.
 14.2.11: Find the limit, if it exists, or show that the limit does not exist.
 14.2.12: Find the limit, if it exists, or show that the limit does not exist.
 14.2.13: Find the limit, if it exists, or show that the limit does not exist.
 14.2.14: Find the limit, if it exists, or show that the limit does not exist.
 14.2.15: Find the limit, if it exists, or show that the limit does not exist.
 14.2.16: Find the limit, if it exists, or show that the limit does not exist.
 14.2.17: Find the limit, if it exists, or show that the limit does not exist.
 14.2.18: Find the limit, if it exists, or show that the limit does not exist.
 14.2.19: Find the limit, if it exists, or show that the limit does not exist.
 14.2.20: Find the limit, if it exists, or show that the limit does not exist.
 14.2.21: Find the limit, if it exists, or show that the limit does not exist.
 14.2.22: Find the limit, if it exists, or show that the limit does not exist.
 14.2.23: Use a computer graph of the function to explain why the limit does ...
 14.2.24: Use a computer graph of the function to explain why the limit does ...
 14.2.25: Find and the set on which is continuous.
 14.2.26: Find and the set on which is continuous.
 14.2.27: Graph the function and observe where it is discontinuous. Then use ...
 14.2.28: Graph the function and observe where it is discontinuous. Then use ...
 14.2.29: Determine the set of points at which the function is continuous.
 14.2.30: Determine the set of points at which the function is continuous.
 14.2.31: Determine the set of points at which the function is continuous.
 14.2.32: Determine the set of points at which the function is continuous.
 14.2.33: Determine the set of points at which the function is continuous.
 14.2.34: Determine the set of points at which the function is continuous.
 14.2.35: Determine the set of points at which the function is continuous.
 14.2.36: Determine the set of points at which the function is continuous.
 14.2.37: Determine the set of points at which the function is continuous.
 14.2.38: Determine the set of points at which the function is continuous.
 14.2.39: Use polar coordinates to find the limit. [If are polar coordinates ...
 14.2.40: Use polar coordinates to find the limit. [If are polar coordinates ...
 14.2.41: Use polar coordinates to find the limit. [If are polar coordinates ...
 14.2.42: At the beginning of this section we considered the function and gue...
 14.2.43: Graph and discuss the continuity of the function
 14.2.44: Let (a) Show that as along any path through of the form with . (b) ...
 14.2.45: Show that the function given by is continuous on . [Hint: Consider .]
 14.2.46: If , show that the function f given by is continuous on .
Solutions for Chapter 14.2: LIMITS AND CONTINUITY
Full solutions for Multivariable Calculus,  7th Edition
ISBN: 9780538497879
Solutions for Chapter 14.2: LIMITS AND CONTINUITY
Get Full SolutionsSince 46 problems in chapter 14.2: LIMITS AND CONTINUITY have been answered, more than 23579 students have viewed full stepbystep solutions from this chapter. Chapter 14.2: LIMITS AND CONTINUITY includes 46 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Multivariable Calculus, was written by and is associated to the ISBN: 9780538497879. This textbook survival guide was created for the textbook: Multivariable Calculus,, edition: 7.

Arccotangent function
See Inverse cotangent function.

Arcsine function
See Inverse sine function.

Boxplot (or boxandwhisker plot)
A graph that displays a fivenumber summary

Constant function (on an interval)
ƒ(x 1) = ƒ(x 2) x for any x1 and x2 (in the interval)

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

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Lemniscate
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.

Linear regression
A procedure for finding the straight line that is the best fit for the data

Normal distribution
A distribution of data shaped like the normal curve.

Numerical model
A model determined by analyzing numbers or data in order to gain insight into a phenomenon, p. 64.

Perihelion
The closest point to the Sun in a planet’s orbit.

Root of a number
See Principal nth root.

Secant
The function y = sec x.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Stretch of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal stretch) by the constant 1/c, or all of the ycoordinates (vertical stretch) of the points by a constant c, c, > 1.

Sum of functions
(ƒ + g)(x) = ƒ(x) + g(x)

Terminal side of an angle
See Angle.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Venn diagram
A visualization of the relationships among events within a sample space.

yaxis
Usually the vertical coordinate line in a Cartesian coordinate system with positive direction up, pp. 12, 629.