 4.1.1: True or False? The Linear Approximation says that the vertical chan...
 4.1.2: Estimate g(1.2) g(1) if g (1) = 4.
 4.1.3: Estimate f (2.1) if f (2) = 1 and f (2) = 3.
 4.1.4: Complete the following sentence: The Linear Approximation shows tha...
 4.1.5: In Exercises 16, use Eq. (2) to estimate f = f (3.02) f (3).f (x) =...
 4.1.6: In Exercises 16, use Eq. (2) to estimate f = f (3.02) f (3).f (x) =...
 4.1.7: The cube root of 27 is 3. How much larger is the cube root of 27.2?...
 4.1.8: Estimate ln(e3 + 0.1) ln(e3) using differentials.
 4.1.9: In Exercises 912, use Eq. (2) to estimate f . Use a calculator to c...
 4.1.10: In Exercises 912, use Eq. (2) to estimate f . Use a calculator to c...
 4.1.11: In Exercises 912, use Eq. (2) to estimate f . Use a calculator to c...
 4.1.12: In Exercises 912, use Eq. (2) to estimate f . Use a calculator to c...
 4.1.13: In Exercises 1316, estimate y using differentials [Eq. (4)]. y = co...
 4.1.14: In Exercises 1316, estimate y using differentials [Eq. (4)]. y = ta...
 4.1.15: In Exercises 1316, estimate y using differentials [Eq. (4)]. y = 10...
 4.1.16: In Exercises 1316, estimate y using differentials [Eq. (4)]. y = x1...
 4.1.17: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.18: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.19: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.20: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.21: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.22: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.23: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.24: In Exercises 1724, estimate using the Linear Approximation and find...
 4.1.25: Estimate f (4.03) for f (x) as in Figure 8. x y (4, 2) (10, 4) y = ...
 4.1.26: At a certain moment, an object in linear motion has velocity 100 m/...
 4.1.27: Which is larger: 2.1 2 or 9.1 9? Explain using the Linear Approxima...
 4.1.28: Estimate sin 61 sin 60 using the Linear Approximation. Hint: Expres...
 4.1.29: Box office revenue at a multiplex cinema in Paris is R(p) = 3600p 1...
 4.1.30: The stopping distance for an automobile is F (s) = 1.1s + 0.054s2 f...
 4.1.31: A thin silver wire has length L = 18 cm when the temperature is T =...
 4.1.32: At a certain moment, the temperature in a snake cage satisfies dT /...
 4.1.33: The atmospheric pressure at altitude h (kilometers) for 11 h 25 is ...
 4.1.34: The resistance R of a copper wire at temperature T = 20C is R = 15 ...
 4.1.35: Newtons Law of Gravitation shows that if a person weighs w pounds o...
 4.1.36: Using Exercise 35(a), estimate the altitude at which a 130lb pilot...
 4.1.37: A stone tossed vertically into the air with initial velocity v cm/s...
 4.1.38: The side s of a square carpet is measured at 6 m. Estimate the maxi...
 4.1.39: In Exercises 39 and 40, use the following fact derived from Newtons...
 4.1.40: Estimate s if = 34, v = 25 ft/s, and v = 2. 4
 4.1.41: The radius of a spherical ball is measured at r = 25 cm. Estimate t...
 4.1.42: The dosage D of diphenhydramine for a dog of body mass w kg is D = ...
 4.1.43: The volume (in liters) and pressure P (in atmospheres) of a certain...
 4.1.44: In the notation of Exercise 43, assume that a measurement yields V ...
 4.1.45: In Exercises 4554, find the linearization at x = a. 45. f (x) = x4,...
 4.1.46: In Exercises 4554, find the linearization at x = a.f (x) = 1 x , a = 2
 4.1.47: In Exercises 4554, find the linearization at x = a.f ( ) = sin2 , a...
 4.1.48: In Exercises 4554, find the linearization at x = a.g(x) = x2 x 3 , ...
 4.1.49: In Exercises 4554, find the linearization at x = a.y = (1 + x)1/2, a =
 4.1.50: In Exercises 4554, find the linearization at x = a.y = (1 + x)1/2, ...
 4.1.51: In Exercises 4554, find the linearization at x = a.y = (1 + x2)1/2,...
 4.1.52: In Exercises 4554, find the linearization at x = a.y = tan1 x, a = 1
 4.1.53: In Exercises 4554, find the linearization at x = a.y = e x , a = 1
 4.1.54: In Exercises 4554, find the linearization at x = a.y = ex ln x, a = 1
 4.1.55: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?
 4.1.56: Compute the linearization of f (x) = 3x 4 at a = 0 and a = 2. Prove...
 4.1.57: Estimate 16.2 using the linearization L(x) of f (x) = x at a = 16. ...
 4.1.58: Estimate 1/ 15 using a suitable linearization of f (x) = 1/ x. Plot...
 4.1.59: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.60: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.61: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.62: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.63: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.64: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.65: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.66: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.67: In Exercises 5967, approximate using linearization and use a calcul...
 4.1.68: Compute the linearization L(x) of f (x) = x2 x3/2 at a = 4. Then pl...
 4.1.69: Show that the Linear Approximation to f (x) = x at x = 9 yields the...
 4.1.70: The LinearApproximation to f (x) = tan x at x = 4 yields the estima...
 4.1.71: Compute dy/dx at the pointP = (2, 1) on the curve y3 + 3xy = 7 and ...
 4.1.72: Apply the method of Exercise 71 to P = (0.5, 1) on y5 + y 2x = 1 to...
 4.1.73: Apply the method of Exercise 71 to P = (1, 2) on y4 + 7xy = 2 to es...
 4.1.74: Show that for any real number k, (1 + x)k 1 + kx for small x. Estim...
 4.1.75: Let f = f (5 + h) f (5), where f (x) = x2. Verify directly that E =...
 4.1.76: Let f = f (1 + h) f (1), where f (x) = x1. Show directly that E = ...
Solutions for Chapter 4.1: Linear Approximation and Applications
Full solutions for Calculus: Early Transcendentals  3rd Edition
ISBN: 9781464114885
Solutions for Chapter 4.1: Linear Approximation and Applications
Get Full SolutionsChapter 4.1: Linear Approximation and Applications includes 76 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781464114885. This 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 76 problems in chapter 4.1: Linear Approximation and Applications have been answered, more than 40786 students have viewed full stepbystep solutions from this chapter.

Algebraic model
An equation that relates variable quantities associated with phenomena being studied

Combination
An arrangement of elements of a set, in which order is not important

Equivalent arrows
Arrows that have the same magnitude and direction.

Event
A subset of a sample space.

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

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Identity matrix
A square matrix with 1’s in the main diagonal and 0’s elsewhere, p. 534.

Index
See Radical.

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Polar equation
An equation in r and ?.

Quadric surface
The graph in three dimensions of a seconddegree equation in three variables.

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

Reference triangle
For an angle ? in standard position, a reference triangle is a triangle formed by the terminal side of angle ?, the xaxis, and a perpendicular dropped from a point on the terminal side to the xaxis. The angle in a reference triangle at the origin is the reference angle

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Slope
Ratio change in y/change in x

Standard form of a complex number
a + bi, where a and b are real numbers

Stem
The initial digit or digits of a number in a stemplot.

Sum of an infinite geometric series
Sn = a 1  r , r 6 1

Zero factorial
See n factorial.