 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: 34 Use a table of numerical values of for near the origin to make a...
 14.2.4: 34 Use a table of numerical values of for near the origin to make a...
 14.2.5: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.6: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.7: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.8: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.9: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.10: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.11: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.12: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.13: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.14: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.15: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.16: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.17: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.18: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.19: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.20: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.21: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.22: 522 Find the limit, if it exists, or show that the limit does not e...
 14.2.23: 2324 Use a computer graph of the function to explain why the limit ...
 14.2.24: 2324 Use a computer graph of the function to explain why the limit ...
 14.2.25: 2526 Find and the set on which istt t f x, y 2x 3y 6 2 st
 14.2.26: 2526 Find and the set on which isf x, y 1 xy1 x 2 y 2 tt
 14.2.27: 2728 Graph the function and observe where it is discontinuous. Then...
 14.2.28: 2728 Graph the function and observe where it is discontinuous. Then...
 14.2.29: 2938 Determine the set of points at which the function is continuou...
 14.2.30: 2938 Determine the set of points at which the function is continuou...
 14.2.31: Fx, y 1 x 2 y 2 1 x 2 y 2 Hx, y
 14.2.32: Hx, y e x ey exy 1 Gx,
 14.2.33: Gx, y lnx 2 y 2 4 Gx, y
 14.2.34: Gx, y tan1 (x y 2 ) fx
 14.2.35: fx, y, z arcsinx 2 y 2 z 2 fx,
 14.2.36: fx, y, z sy x 2 ln z f x
 14.2.37: f x, y 1 x 2 y 3 2x 2 y 2 if if x, y 0, 0 x, y 0, 0 f x, y 0 x
 14.2.38: f x, y 0 xy x 2 xy y 2 if if x, y 0, 0 x, y 0, 0 hx, y t f x,
 14.2.39: 39 41 Use polar coordinates to find the limit. [If are polar coordi...
 14.2.40: 39 41 Use polar coordinates to find the limit. [If are polar coordi...
 14.2.41: 39 41 Use polar coordinates to find the limit. [If are polar coordi...
 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 functionfx, y 1sin xyxyifif...
 14.2.44: Let(a) Show that as along any paththrough of the form with .(b) Des...
 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 Calculus: Early Transcendentals  7th Edition
ISBN: 9780538497909
Solutions for Chapter 14.2: Limits and Continuity
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 46 problems in chapter 14.2: Limits and Continuity have been answered, more than 33119 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 7. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780538497909. Chapter 14.2: Limits and Continuity includes 46 full stepbystep solutions.

Center
The central point in a circle, ellipse, hyperbola, or sphere

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Data
Facts collected for statistical purposes (singular form is datum)

Empty set
A set with no elements

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Horizontal asymptote
The line is a horizontal asymptote of the graph of a function ƒ if lim x: q ƒ(x) = or lim x: q ƒ(x) = b

Integers
The numbers . . ., 3, 2, 1, 0,1,2,...2

Inverse function
The inverse relation of a onetoone function.

Inverse secant function
The function y = sec1 x

Law of sines
sin A a = sin B b = sin C c

Local extremum
A local maximum or a local minimum

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Power rule of logarithms
logb Rc = c logb R, R 7 0.

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

Pseudorandom numbers
Computergenerated numbers that can be used to approximate true randomness in scientific studies. Since they depend on iterative computer algorithms, they are not truly random

Quartic function
A degree 4 polynomial function.

Reciprocal function
The function ƒ(x) = 1x

Sequence of partial sums
The sequence {Sn} , where Sn is the nth partial sum of the series, that is, the sum of the first n terms of the series.

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Zero factorial
See n factorial.