 11.1.1: (a) What is a sequence? (b) What does it mean to say that limnl` an...
 11.1.2: (a) What is a convergent sequence? Give two examples. (b) What is a...
 11.1.3: 312 List the first five terms of the sequence.
 11.1.4: 312 List the first five terms of the sequence.
 11.1.5: 312 List the first five terms of the sequence.
 11.1.6: 312 List the first five terms of the sequence.
 11.1.7: 312 List the first five terms of the sequence.
 11.1.8: 312 List the first five terms of the sequence.
 11.1.9: 312 List the first five terms of the sequence.
 11.1.10: 312 List the first five terms of the sequence.
 11.1.11: 312 List the first five terms of the sequence.
 11.1.12: 312 List the first five terms of the sequence.
 11.1.13: 1318 Find a formula for the general term an of the sequence, assumi...
 11.1.14: 1318 Find a formula for the general term an of the sequence, assumi...
 11.1.15: 1318 Find a formula for the general term an of the sequence, assumi...
 11.1.16: 1318 Find a formula for the general term an of the sequence, assumi...
 11.1.17: 1318 Find a formula for the general term an of the sequence, assumi...
 11.1.18: 1318 Find a formula for the general term an of the sequence, assumi...
 11.1.19: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.20: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.21: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.22: 1922 Calculate, to four decimal places, the first ten terms of the ...
 11.1.23: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.24: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.25: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.26: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.27: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.28: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.29: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.30: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.31: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.32: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.33: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.34: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.35: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.36: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.37: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.38: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.39: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.40: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.41: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.42: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.43: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.44: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.45: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.46: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.47: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.48: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.49: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.50: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.51: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.52: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.53: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.54: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.55: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.56: 2356 Determine whether the sequence converges or diverges. If it co...
 11.1.57: 5763 Use a graph of the sequence to decide whether the sequence is ...
 11.1.58: A curve called the folium of Descartes is defined by the parametric...
 11.1.59: 5763 Use a graph of the sequence to decide whether the sequence is ...
 11.1.60: 5763 Use a graph of the sequence to decide whether the sequence is ...
 11.1.61: 5763 Use a graph of the sequence to decide whether the sequence is ...
 11.1.62: 5763 Use a graph of the sequence to decide whether the sequence is ...
 11.1.63: 5763 Use a graph of the sequence to decide whether the sequence is ...
 11.1.64: (a) Determine whether the sequence defined as follows is convergent...
 11.1.65: If $1000 is invested at 6% interest, compounded annually, then afte...
 11.1.66: If you deposit $100 at the end of every month into an account that ...
 11.1.67: A fish farmer has 5000 catfish in his pond. The number of catfish i...
 11.1.68: Find the first 40 terms of the sequence defined by an11 H 1 2 an 3a...
 11.1.69: For what values of r is the sequence hnr n j convergent?
 11.1.70: (a) If han j is convergent, show that lim n l` an11 lim n l` an (b)...
 11.1.71: Suppose you know that han j is a decreasing sequence and all its te...
 11.1.72: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.73: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.74: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.75: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.76: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.77: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.78: 7278 Determine whether the sequence is increasing, decreasing, or n...
 11.1.79: Find the limit of the sequence 5s2 , s2s2 , s2s2s2 , . . .6
 11.1.80: A sequence han j is given by a1 s2 , an11 s2 1 an . (a) By inductio...
 11.1.81: Show that the sequence defined by a1 1 an11 3 2 1 an is increasing ...
 11.1.82: Show that the sequence defined by a1 2 an11 1 3 2 an satisfies 0 , ...
 11.1.83: (a) Fibonacci posed the following problem: Suppose that rabbits liv...
 11.1.84: (a) Let a1 a, a2 fsad, a3 fsa2d fs fsadd, . . . , an11 fsan d, wher...
 11.1.85: (a) Use a graph to guess the value of the limit lim nl` n5 n! (b) U...
 11.1.86: Use Definition 2 directly to prove that limn l ` r n 0 when  r , 1.
 11.1.87: Prove Theorem 6. [Hint: Use either Definition 2 or the Squeeze Theo...
 11.1.88: Prove Theorem 7.
 11.1.89: Prove that if limnl` an 0 and hbnj is bounded, then limnl` san bnd 0.
 11.1.90: Let an S1 1 1 n D n . (a) Show that if 0 < a , b, then bn11 2 an11 ...
 11.1.91: Let a and b be positive numbers with a . b. Let a1 be their arithme...
 11.1.92: (a) Show that if limn l ` a2n L and limn l ` a2n11 L, then han j is...
 11.1.93: The size of an undisturbed fish population has been modeled by the ...
Solutions for Chapter 11.1: Sequences
Full solutions for Single Variable Calculus: Early Transcendentals  8th Edition
ISBN: 9781305270336
Solutions for Chapter 11.1: Sequences
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 93 problems in chapter 11.1: Sequences have been answered, more than 112426 students have viewed full stepbystep solutions from this chapter. Chapter 11.1: Sequences includes 93 full stepbystep solutions. This textbook survival guide was created for the textbook: Single Variable Calculus: Early Transcendentals, edition: 8. Single Variable Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781305270336.

Base
See Exponential function, Logarithmic function, nth power of a.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Constant term
See Polynomial function

Fibonacci numbers
The terms of the Fibonacci sequence.

Focal length of a parabola
The directed distance from the vertex to the focus.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Inverse composition rule
The composition of a onetoone function with its inverse results in the identity function.

Nappe
See Right circular cone.

Natural numbers
The numbers 1, 2, 3, . . . ,.

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

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Rational zeros
Zeros of a function that are rational numbers.

Reference angle
See Reference triangle

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Sphere
A set of points in Cartesian space equally distant from a fixed point called the center.

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Third quartile
See Quartile.

xcoordinate
The directed distance from the yaxis yzplane to a point in a plane (space), or the first number in an ordered pair (triple), pp. 12, 629.

Zero factor property
If ab = 0 , then either a = 0 or b = 0.