 1.4.1: The definition of a twosided limit states: limxa f(x) = Lif given ...
 1.4.2: Suppose that f(x) is a function such that for any given > 0, the co...
 1.4.3: Suppose that is any positive number. Find the largest valueof such ...
 1.4.4: The definition of limit at + states: limx+ f(x) = Lif given any num...
 1.4.5: Find the smallest positive number N such that for eachx>N, the valu...
 1.4.6: Use the method of Exercise 5 to find a number such that5x + 1 4 <...
 1.4.7: Let f(x) = x + x withL = limx1 f(x) and let = 0.2.Use a graphing ut...
 1.4.8: Let f(x) = (sin 2x)/x and use a graphing utility to conjecturethe v...
 1.4.9: 916 A positive number and the limit L of a function f at a are give...
 1.4.10: 916 A positive number and the limit L of a function f at a are give...
 1.4.11: 916 A positive number and the limit L of a function f at a are give...
 1.4.12: 916 A positive number and the limit L of a function f at a are give...
 1.4.13: 916 A positive number and the limit L of a function f at a are give...
 1.4.14: 916 A positive number and the limit L of a function f at a are give...
 1.4.15: 916 A positive number and the limit L of a function f at a are give...
 1.4.16: 916 A positive number and the limit L of a function f at a are give...
 1.4.17: 1726 Use Definition 1.4.1 to prove that the limit is correct. . lim...
 1.4.18: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx4...
 1.4.19: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx5...
 1.4.20: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx1...
 1.4.21: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx0...
 1.4.22: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx3...
 1.4.23: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx1...
 1.4.24: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx2...
 1.4.25: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx0...
 1.4.26: 1726 Use Definition 1.4.1 to prove that the limit is correct. limx2...
 1.4.27: Give rigorous definitions of limxa+ f(x) = L and limxa f(x) = L.
 1.4.28: Consider the statement that limxa f(x) L = 0.(a) Using Definition...
 1.4.29: (a) Show that(3x2 + 2x 20) 300=3x + 32x 10(b) Find an upper b...
 1.4.30: . (a) Show that283x + 1 4 =123x + 1 x 2(b) Is 12/(3x + 1) bounded...
 1.4.31: 3136 Use Definition 1.4.1 to prove that the stated limit iscorrect....
 1.4.32: 3136 Use Definition 1.4.1 to prove that the stated limit iscorrect....
 1.4.33: 3136 Use Definition 1.4.1 to prove that the stated limit iscorrect....
 1.4.34: 3136 Use Definition 1.4.1 to prove that the stated limit iscorrect....
 1.4.35: 3136 Use Definition 1.4.1 to prove that the stated limit iscorrect....
 1.4.36: 3136 Use Definition 1.4.1 to prove that the stated limit iscorrect....
 1.4.37: Letf(x) =0, if x is rationalx, if x is irrationalUse Definition 1.4...
 1.4.38: Letf(x) =0, if x is rational1, if x is irrationalUse Definition 1.4...
 1.4.39: (a) Find the smallest positive number N such that for eachx in the ...
 1.4.40: In each part, find the smallest positive value of N such thatfor ea...
 1.4.41: (a) Find the values of x1 and x2 in the accompanying figure.(b) Fin...
 1.4.42: (a) Find the values of x1 and x2 in the accompanying figure.(b) Fin...
 1.4.43: 4346 A positive number and the limitLof a function f at+ are given....
 1.4.44: 4346 A positive number and the limitLof a function f at+ are given....
 1.4.45: 4346 A positive number and the limitLof a function f at+ are given....
 1.4.46: 4346 A positive number and the limitLof a function f at+ are given....
 1.4.47: 4750 A positive number and the limitLof a function f at are given. ...
 1.4.48: 4750 A positive number and the limitLof a function f at are given. ...
 1.4.49: 4750 A positive number and the limitLof a function f at are given. ...
 1.4.50: 4750 A positive number and the limitLof a function f at are given. ...
 1.4.51: 5156 Use Definition 1.4.2 or 1.4.3 to prove that the stated limit i...
 1.4.52: 5156 Use Definition 1.4.2 or 1.4.3 to prove that the stated limit i...
 1.4.53: 5156 Use Definition 1.4.2 or 1.4.3 to prove that the stated limit i...
 1.4.54: 5156 Use Definition 1.4.2 or 1.4.3 to prove that the stated limit i...
 1.4.55: 5156 Use Definition 1.4.2 or 1.4.3 to prove that the stated limit i...
 1.4.56: 5156 Use Definition 1.4.2 or 1.4.3 to prove that the stated limit i...
 1.4.57: (a) Find the largest open interval, centered at the origin onthe x...
 1.4.58: In each part, find the largest open interval centered at x = 1,such...
 1.4.59: 5964 Use Definition 1.4.4 or 1.4.5 to prove that the stated limit i...
 1.4.60: 5964 Use Definition 1.4.4 or 1.4.5 to prove that the stated limit i...
 1.4.61: 5964 Use Definition 1.4.4 or 1.4.5 to prove that the stated limit i...
 1.4.62: 5964 Use Definition 1.4.4 or 1.4.5 to prove that the stated limit i...
 1.4.63: 5964 Use Definition 1.4.4 or 1.4.5 to prove that the stated limit i...
 1.4.64: 5964 Use Definition 1.4.4 or 1.4.5 to prove that the stated limit i...
 1.4.65: 6570 Use the definitions in Exercise 27 to prove that the stated on...
 1.4.66: 6570 Use the definitions in Exercise 27 to prove that the stated on...
 1.4.67: 6570 Use the definitions in Exercise 27 to prove that the stated on...
 1.4.68: 6570 Use the definitions in Exercise 27 to prove that the stated on...
 1.4.69: 6570 Use the definitions in Exercise 27 to prove that the stated on...
 1.4.70: 6570 Use the definitions in Exercise 27 to prove that the stated on...
 1.4.71: 7174 Write out the definition for the corresponding limit in the ma...
 1.4.72: 7174 Write out the definition for the corresponding limit in the ma...
 1.4.73: 7174 Write out the definition for the corresponding limit in the ma...
 1.4.74: 7174 Write out the definition for the corresponding limit in the ma...
 1.4.75: According to Ohms law, when a voltage of V volts is appliedacross a...
 1.4.76: Writing Compare informal Definition 1.1.1 with Definition1.4.1.(a) ...
 1.4.77: Writing Compare informal Definition 1.3.1 with Definition1.4.2.(a) ...
Solutions for Chapter 1.4: LIMITS (DISCUSSED MORE RIGOROUSLY)
Full solutions for Calculus: Early Transcendentals,  10th Edition
ISBN: 9780470647691
Solutions for Chapter 1.4: LIMITS (DISCUSSED MORE RIGOROUSLY)
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Chapter 1.4: LIMITS (DISCUSSED MORE RIGOROUSLY) includes 77 full stepbystep solutions. Calculus: Early Transcendentals, was written by and is associated to the ISBN: 9780470647691. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, , edition: 10. Since 77 problems in chapter 1.4: LIMITS (DISCUSSED MORE RIGOROUSLY) have been answered, more than 36596 students have viewed full stepbystep solutions from this chapter.

Absolute value of a real number
Denoted by a, represents the number a or the positive number a if a < 0.

Arccosine function
See Inverse cosine function.

Central angle
An angle whose vertex is the center of a circle

Convenience sample
A sample that sacrifices randomness for convenience

Elimination method
A method of solving a system of linear equations

End behavior
The behavior of a graph of a function as.

Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.

Exponential form
An equation written with exponents instead of logarithms.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

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

Mode of a data set
The category or number that occurs most frequently in the set.

Monomial function
A polynomial with exactly one term.

Multiplication property of equality
If u = v and w = z, then uw = vz

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

Origin
The number zero on a number line, or the point where the x and yaxes cross in the Cartesian coordinate system, or the point where the x, y, and zaxes cross in Cartesian threedimensional space

Probability of an event in a finite sample space of equally likely outcomes
The number of outcomes in the event divided by the number of outcomes in the sample space.

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Randomization
The principle of experimental design that makes it possible to use the laws of probability when making inferences.

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

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.