 2.8.1: ?Use the given graph to estimate the value of each derivative. Then...
 2.8.2: ?Use the given graph to estimate the value of each derivative. Then...
 2.8.3: ?Match the graph of each function in (a)–(d) with the graph of its ...
 2.8.4: ?Trace or copy the graph of the given function \(f\). (Assume that ...
 2.8.5: ?Trace or copy the graph of the given function \(f\). (Assume that ...
 2.8.6: ?Trace or copy the graph of the given function f. (Assume that the ...
 2.8.7: ?Trace or copy the graph of the given function f. (Assume that the ...
 2.8.8: ?Trace or copy the graph of the given function \(f\). (Assume that ...
 2.8.9: ?Trace or copy the graph of the given function f. (Assume that the ...
 2.8.10: ?Trace or copy the graph of the given function \(f\). (Assume that ...
 2.8.11: ?Trace or copy the graph of the given function \(f\). (Assume that ...
 2.8.12: ?Shown is the graph of the population function \(P(t)\) for yeast c...
 2.8.13: ?A rechargeable battery is plugged into a charger. The graph shows ...
 2.8.14: ?The graph (from the US Department of Energy) shows how driving spe...
 2.8.15: ?The graph shows how the average surface water temperature f of Lak...
 2.8.16: ?Make a careful sketch of the graph of f and below it sketch the gr...
 2.8.17: ?Make a careful sketch of the graph of f and below it sketch the gr...
 2.8.18: ?Make a careful sketch of the graph of f and below it sketch the gr...
 2.8.19: ?Let f(x) = x2.(a) Estimate the values of f’ (0), f’ f’ (1), and f’...
 2.8.20: ?Let f (x) = x3(a) Estimate the values of f’(0), f’(, f’(1), f’(2),...
 2.8.21: ?Find the derivative of the function using the definition of deriva...
 2.8.22: ?Find the derivative of the function using the definition of deriva...
 2.8.23: ?Find the derivative of the function using the definition of deriva...
 2.8.24: ?Find the derivative of the function using the definition of deriva...
 2.8.25: ?Find the derivative of the function using the definition of deriva...
 2.8.26: ?Find the derivative of the function using the definition of deriva...
 2.8.27: ?Find the derivative of the function using the definition of deriva...
 2.8.28: ?Find the derivative of the function using the definition of deriva...
 2.8.29: ?Find the derivative of the function using the definition of deriva...
 2.8.30: ?Find the derivative of the function using the definition of deriva...
 2.8.31: ?Find the derivative of the function using the definition of deriva...
 2.8.32: ?Find the derivative of the function using the definition of deriva...
 2.8.33: ?(a) Sketch the graph of by starting with the graph of y = and usin...
 2.8.34: ?(a) If f (x) = x + 1/x, find f’(x).(b) Check to see that your answ...
 2.8.35: ?(a) If f (x) = x4 + 2x, find f’(x).(b) Check to see that your answ...
 2.8.36: ?The table gives the number N(t), measured in thousands, of minimal...
 2.8.37: ?The table gives the height as time passes of a typical pine tree g...
 2.8.38: ?Water temperature affects the growth rate of brook trout. The tabl...
 2.8.39: ?Let P represent the percentage of a city's electrical power that i...
 2.8.40: ?Suppose N is the number of people in the United States who travel ...
 2.8.41: ?The graph of f is given. State, with reasons, the numbers at which...
 2.8.42: ?The graph of f is given. State, with reasons, the numbers at which...
 2.8.43: ?The graph of f is given. State, with reasons, the numbers at which...
 2.8.44: ?The graph of f is given. State, with reasons, the numbers at which...
 2.8.45: ?Graph the function . Zoom in repeatedly, first toward the point (...
 2.8.46: ?Zoom in toward the points (1, 0),(0, 1), and (1, 0) on the graph ...
 2.8.47: ?The graphs of a function f and its derivative f’ are shown. Which ...
 2.8.48: ?The graphs of a function f and its derivative f’ are shown. Which ...
 2.8.49: ?The figure shows the graphs of f, f’, and f”. Identify each curve,...
 2.8.50: ?The figure shows graphs of f, f’, f”, and f’’’. Identify each curv...
 2.8.51: ?The figure shows the graphs of three functions. One is the positio...
 2.8.52: ?The figure shows the graphs of four functions. One is the position...
 2.8.53: ?Use the definition of a derivative to find f’(x) and f’’(x). Then ...
 2.8.54: ?Use the definition of a derivative to find f’(x) and f’’(x). Then ...
 2.8.55: ?If f(x) = 2x2  x3, find f’(x), f’’(x), f’’’(x), and f(4)(x). Grap...
 2.8.56: ?(a) The graph of a position function of a car is shown, where s is...
 2.8.57: ?Let f(x) = (a) If a ? 0, use Equation 2.7.5 to find f’(a)..(b) Sho...
 2.8.58: ?1. If g(x) = x2/3, show that g’(0) does not exist.2. If a ? 0, fin...
 2.8.59: ?Show that the function f(x) =  x  6  is not differentiable at 6...
 2.8.60: ?Where is the greatest integer function f(x) = [[ x ]] not differen...
 2.8.61: ?(a) Sketch the graph of the function f(x) = x  x .(b) For what v...
 2.8.62: ?(a) Sketch the graph of the function g(x) = x +  x .(b) For what...
 2.8.63: ?Derivatives of Even and Odd Functions Recall that a function f is ...
 2.8.64: ?Left and RightHand Derivatives The lefthand and righthand deri...
 2.8.65: ?Left and RightHand Derivatives The lefthand and righthand deri...
 2.8.66: ?When you turn on a hotwater faucet, the temperature T of the wate...
 2.8.67: ?Nick starts jogging and runs faster and faster for 3 minutes, then...
 2.8.68: ?Let ? be the tangent line to the parabola y = x2 at the point (1, ...
Solutions for Chapter 2.8: Limits at Infinity; Horizontal Asymptotes
Full solutions for Calculus: Early Transcendentals  9th Edition
ISBN: 9781337613927
Solutions for Chapter 2.8: Limits at Infinity; Horizontal Asymptotes
Get Full SolutionsSummary of Chapter 2.8: Limits at Infinity; Horizontal Asymptotes
We let x approach a number and the result was that the values of y became arbitrarily large (positive or negative). In this section we let x become arbitrarily large ( positive or negative) and see what happens to y.
Since 68 problems in chapter 2.8: Limits at Infinity; Horizontal Asymptotes have been answered, more than 201993 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by Aimee Notetaker and is associated to the ISBN: 9781337613927. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 9. Chapter 2.8: Limits at Infinity; Horizontal Asymptotes includes 68 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions.

Additive identity for the complex numbers
0 + 0i is the complex number zero

Angular speed
Speed of rotation, typically measured in radians or revolutions per unit time

Arcsine function
See Inverse sine function.

Coefficient matrix
A matrix whose elements are the coefficients in a system of linear equations

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

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>

Imaginary axis
See Complex plane.

Implicitly defined function
A function that is a subset of a relation defined by an equation in x and y.

Inductive step
See Mathematical induction.

Infinite limit
A special case of a limit that does not exist.

Initial point
See Arrow.

Logarithmic reexpression of data
Transformation of a data set involving the natural logarithm: exponential regression, natural logarithmic regression, power regression

Objective function
See Linear programming problem.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Radian
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.

Row operations
See Elementary row operations.

Solve by substitution
Method for solving systems of linear equations.

Sum identity
An identity involving a trigonometric function of u + v

Symmetric difference quotient of ƒ at a
ƒ(x + h)  ƒ(x  h) 2h

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