 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 42635 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.

Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point

Average velocity
The change in position divided by the change in time.

Dihedral angle
An angle formed by two intersecting planes,

Direct variation
See Power function.

Distance (on a number line)
The distance between real numbers a and b, or a  b

Ellipse
The set of all points in the plane such that the sum of the distances from a pair of fixed points (the foci) is a constant

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Graphical model
A visible representation of a numerical or algebraic model.

Higherdegree polynomial function
A polynomial function whose degree is ? 3

Inverse secant function
The function y = sec1 x

Irrational numbers
Real numbers that are not rational, p. 2.

Jump discontinuity at x a
limx:a  ƒ1x2 and limx:a + ƒ1x2 exist but are not equal

Linear regression line
The line for which the sum of the squares of the residuals is the smallest possible

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Secant
The function y = sec x.

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

Square matrix
A matrix whose number of rows equals the number of columns.

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Vertex of a cone
See Right circular cone.

Weights
See Weighted mean.