 3.9.1: Find the tangent line approximation for 1 + x nearx = 0.
 3.9.2: What is the tangent line approximation to ex near x = 0?
 3.9.3: Find the tangent line approximation to 1/x near x = 1.
 3.9.4: Find the local linearization of f(x) = x2 near x = 1.
 3.9.5: What is the local linearization of ex2 near x = 1?
 3.9.6: Show that 1 x/2 is the tangent line approximation to1/1 + x near x ...
 3.9.7: Show that ex 1 x near x = 0
 3.9.8: Local linearization gives values too small for the functionx2 and t...
 3.9.9: Using a graph like Figure 3.41, estimate to one decimalplace the ma...
 3.9.10: For x near 0, local linearization givesex 1 + x.Using a graph, deci...
 3.9.11: (a) Find the best linear approximation, L(x), to f(x) =ex near x = ...
 3.9.12: (a) Find the tangent line approximation to cos x at x =/4.(b) Use a...
 3.9.13: (a) Graph f(x) = x3 3x2 + 3x + 1.(b) Find and add to your sketch th...
 3.9.14: (a) Show that 1+kx is the local linearization of(1+x)knear x = 0.(b...
 3.9.15: . Figure 3.43 shows f(x) and its local linearization atx = a. What ...
 3.9.16: In 1617, the equation has a solution near x = 0.By replacing the le...
 3.9.17: In 1617, the equation has a solution near x = 0.By replacing the le...
 3.9.18: (a) Given that f(7) = 13 and f(7) = 0.38, estimatef(7.1).(b) Suppos...
 3.9.19: (a) Explain why the following equation has a solutionnear 0:et = 0....
 3.9.20: The speed of sound in dry air isf(T ) = 331.31 + T273.15 meters/sec...
 3.9.21: Air pressure at sea level is 30 inches of mercury. At analtitude of...
 3.9.22: On October 7, 2010, the Wall Street Journal8 reportedthat Android c...
 3.9.23: Writing g for the acceleration due to gravity, the period,T , of a ...
 3.9.24: Suppose now the length of the pendulum in remains constant, but tha...
 3.9.25: Suppose f has a continuous positive second derivativefor all x. Whi...
 3.9.26: Suppose f(x) is a differentiable decreasing function forall x. In e...
 3.9.27: 2729 investigate the motion of a projectile shotfrom a cannon. The ...
 3.9.28: 2729 investigate the motion of a projectile shotfrom a cannon. The ...
 3.9.29: 2729 investigate the motion of a projectile shotfrom a cannon. The ...
 3.9.30: In 3032, find the local linearization of f(x) near 0and use this to...
 3.9.31: In 3032, find the local linearization of f(x) near 0and use this to...
 3.9.32: In 3032, find the local linearization of f(x) near 0and use this to...
 3.9.33: In 3337, find a formula for the error E(x) in thetangent line appro...
 3.9.34: In 3337, find a formula for the error E(x) in thetangent line appro...
 3.9.35: In 3337, find a formula for the error E(x) in thetangent line appro...
 3.9.36: In 3337, find a formula for the error E(x) in thetangent line appro...
 3.9.37: In 3337, find a formula for the error E(x) in thetangent line appro...
 3.9.38: Multiply the local linearization of ex near x = 0 by itselfto obtai...
 3.9.39: (a) Show that 1 x is the local linearization of 11 + x near x = 0.(...
 3.9.40: From the local linearizations of ex and sin x near x =0, write down...
 3.9.41: Use local linearization to derive the product rule,[f(x)g(x)] = f(x...
 3.9.42: Derive the chain rule using local linearization. [Hint: Inother wor...
 3.9.43: Consider a function f and a point a. Suppose there is anumber L suc...
 3.9.44: Consider the graph of f(x) = x2 near x = 1. Find aninterval around ...
 3.9.45: In 4546, explain what is wrong with the statement.To approximate f(...
 3.9.46: In 4546, explain what is wrong with the statement.The linear approx...
 3.9.47: In 4749, give an example of:Two different functions that have the s...
 3.9.48: In 4749, give an example of:A nonpolynomial function that has the ...
 3.9.49: In 4749, give an example of:A function that does not have a linear ...
 3.9.50: Let f be a differentiable function and let L be the linearfunction ...
Solutions for Chapter 3.9: LINEAR APPROXIMATION AND THE DERIVATIVE
Full solutions for Calculus: Single and Multivariable  6th Edition
ISBN: 9780470888612
Solutions for Chapter 3.9: LINEAR APPROXIMATION AND THE DERIVATIVE
Get Full SolutionsCalculus: Single and Multivariable was written by and is associated to the ISBN: 9780470888612. This expansive textbook survival guide covers the following chapters and their solutions. Since 50 problems in chapter 3.9: LINEAR APPROXIMATION AND THE DERIVATIVE have been answered, more than 42389 students have viewed full stepbystep solutions from this chapter. Chapter 3.9: LINEAR APPROXIMATION AND THE DERIVATIVE includes 50 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus: Single and Multivariable , edition: 6.

artesian coordinate system
An association between the points in a plane and ordered pairs of real numbers; or an association between the points in threedimensional space and ordered triples of real numbers

Combinations of n objects taken r at a time
There are nCr = n! r!1n  r2! such combinations,

Compounded monthly
See Compounded k times per year.

Damping factor
The factor Aea in an equation such as y = Aeat cos bt

Data
Facts collected for statistical purposes (singular form is datum)

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

DMS measure
The measure of an angle in degrees, minutes, and seconds

Halfangle identity
Identity involving a trigonometric function of u/2.

Identity function
The function ƒ(x) = x.

Imaginary axis
See Complex plane.

Interval
Connected subset of the real number line with at least two points, p. 4.

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Multiplicative inverse of a complex number
The reciprocal of a + bi, or 1 a + bi = a a2 + b2 ba2 + b2 i

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Probability simulation
A numerical simulation of a probability experiment in which assigned numbers appear with the same probabilities as the outcomes of the experiment.

Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc  ad c2 + d2 i

Real number line
A horizontal line that represents the set of real numbers.

Standard representation of a vector
A representative arrow with its initial point at the origin

Standard unit vectors
In the plane i = <1, 0> and j = <0,1>; in space i = <1,0,0>, j = <0,1,0> k = <0,0,1>

Subtraction
a  b = a + (b)