 2.7.1: Assume that lim x f (x) = L and limxL g(x) = Which of the following...
 2.7.2: What are the following limits? (a) lim x x3 (b) lim x x3 (c) lim x x4
 2.7.3: Sketch the graph of a function that approaches a limit as x but doe...
 2.7.4: What is the sign of a if f (x) = ax3 + x + 1 satisfies lim x f (x) = ?
 2.7.5: What is the sign of the coefficient multiplying x7 if f is a polyno...
 2.7.6: Explain why lim x sin 1 x exists but limx0 sin 1 x does not exist. ...
 2.7.7: In Exercises 716, evaluate the limit. lim x x x + 9
 2.7.8: In Exercises 716, evaluate the limit. lim x 3x2 + 20x 4x2 + 9
 2.7.9: In Exercises 716, evaluate the limit. lim x 3x2 + 20x 2x4 + 3x3 29
 2.7.10: In Exercises 716, evaluate the limit. lim x 4 x + 5
 2.7.11: In Exercises 716, evaluate the limit. lim x 7x 9 4x + 3
 2.7.12: In Exercises 716, evaluate the limit. lim x 9x2 2 6 29x
 2.7.13: In Exercises 716, evaluate the limit. lim x 7x2 9 4x + 3
 2.7.14: In Exercises 716, evaluate the limit. lim x 5x 9 4x3 + 2x + 7
 2.7.15: In Exercises 716, evaluate the limit. lim x 3x3 10 x + 4
 2.7.16: In Exercises 716, evaluate the limit. lim x 2x5 + 3x4 31x 8x4 31x2 ...
 2.7.17: In Exercises 1722, find the horizontal asymptotes. f (x) = 2x2 3x 8...
 2.7.18: In Exercises 1722, find the horizontal asymptotes. f (x) = 8x3 x2 7...
 2.7.19: In Exercises 1722, find the horizontal asymptotes. f (x) = 36x2 + 7...
 2.7.20: In Exercises 1722, find the horizontal asymptotes. f (x) = 36x4 + 7...
 2.7.21: In Exercises 1722, find the horizontal asymptotes. f (t) = et 1 + et
 2.7.22: In Exercises 1722, find the horizontal asymptotes. f (t) = t1/3 (64...
 2.7.23: In Exercises 2330, evaluate the limit. lim x 9x4 + 3x + 2 4x3 + 1
 2.7.24: In Exercises 2330, evaluate the limit. lim x x3 + 20x 10x 2
 2.7.25: In Exercises 2330, evaluate the limit. x 8x2 + 7x1/3 16x4 + 6
 2.7.26: In Exercises 2330, evaluate the limit. lim x 4x 3 25x2 + 4x
 2.7.27: In Exercises 2330, evaluate the limit. lim t t4/3 + t1/3 (4t2/3 + 1)2
 2.7.28: In Exercises 2330, evaluate the limit. lim t t4/3 9t1/3 (8t4 + 2)1/3
 2.7.29: In Exercises 2330, evaluate the limit. lim x x + x x + 1
 2.7.30: In Exercises 2330, evaluate the limit. lim t 4 + 6e2t 5 9e3t
 2.7.31: Determine lim x tan1 x. Explain geometrically.
 2.7.32: Show that lim x( x2 + 1 x) = 0. Hint: Observe that x2 + 1 x = 1 x2 ...
 2.7.33: According to the MichaelisMenten equation (Figure 7), when an enzym...
 2.7.34: Suppose that the average temperature of Earth is T (t) = 283 + 3(1 ...
 2.7.35: In Exercises 3542, calculate the limit.. lim x( 4x4 + 9x 2x2)
 2.7.36: In Exercises 3542, calculate the limit. lim x( 9x3 + x x3/2)
 2.7.37: In Exercises 3542, calculate the limit. lim x(2 x x + 2)
 2.7.38: In Exercises 3542, calculate the limit. lim x 1 x 1 x + 2
 2.7.39: In Exercises 3542, calculate the limit. lim x (ln(3x + 1) ln(2x + 1))
 2.7.40: In Exercises 3542, calculate the limit. lim x ln( 5x2 + 2) ln x
 2.7.41: In Exercises 3542, calculate the limit. lim x tan1 x2 + 9 9 x
 2.7.42: In Exercises 3542, calculate the limit. lim x tan1 1 + x 1 x
 2.7.43: Let P (n) be the perimeter of an ngon inscribed in a unit circle (...
 2.7.44: Physicists have observed that Einsteins theory of special relativit...
 2.7.45: Every limit as x can be rewritten as a onesided limit as t 0+, whe...
 2.7.46: Rewrite the following as onesided limits as in Exercise 45 and eva...
 2.7.47: Let G(b) = lim x(1 + bx ) 1/x for b 0. Investigate G(b) numerically...
Solutions for Chapter 2.7: Limits at Infinity
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 2.7: Limits at Infinity
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals , edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Since 47 problems in chapter 2.7: Limits at Infinity have been answered, more than 40779 students have viewed full stepbystep solutions from this chapter. Chapter 2.7: Limits at Infinity includes 47 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885.

Ambiguous case
The case in which two sides and a nonincluded angle can determine two different triangles

Annual percentage yield (APY)
The rate that would give the same return if interest were computed just once a year

Arcsecant function
See Inverse secant function.

Bias
A flaw in the design of a sampling process that systematically causes the sample to differ from the population with respect to the statistic being measured. Undercoverage bias results when the sample systematically excludes one or more segments of the population. Voluntary response bias results when a sample consists only of those who volunteer their responses. Response bias results when the sampling design intentionally or unintentionally influences the responses

Coefficient of determination
The number r2 or R2 that measures how well a regression curve fits the data

Coordinate(s) of a point
The number associated with a point on a number line, or the ordered pair associated with a point in the Cartesian coordinate plane, or the ordered triple associated with a point in the Cartesian threedimensional space

Dihedral angle
An angle formed by two intersecting planes,

Event
A subset of a sample space.

Explicitly defined sequence
A sequence in which the kth term is given as a function of k.

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.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Midpoint (in Cartesian space)
For the line segment with endpoints (x 1, y1, z 1) and (x2, y2, z2), ax 1 + x 22 ,y1 + y22 ,z 1 + z 22 b

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

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Position vector of the point (a, b)
The vector <a,b>.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

Reflection
Two points that are symmetric with respect to a lineor a point.

Slant asymptote
An end behavior asymptote that is a slant line

Spiral of Archimedes
The graph of the polar curve.

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