 3.11.1E: In Exercises 1–5, find the linearization L(x) of ƒ(x) at X = a.
 3.11.2E: In Exercises 1–5, find the linearization L(x) of ƒ(x) at X = a.
 3.11.3E: In Exercises 1–5, find the linearization L(x) of ƒ(x) at X = a.
 3.11.4E: In Exercises 1–5, find the linearization L(x) of ƒ(x) at X = a.
 3.11.5E: In Exercises 1–5, find the linearization L(x) of ƒ(x) at X = a.
 3.11.6E: Common linear approximations at x = 0 Find the linearizations of th...
 3.11.7E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.8E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.9E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.10E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.11E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.12E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.13E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.14E: In Exercises 7–14, find a linearization at a suitably chosen intege...
 3.11.15E: Show that the linearization of ƒ(x) = (1 + x)k at x = 0 is L(x) = 1...
 3.11.16E: Use the linear approximation to find an approximation for the funct...
 3.11.17E: Faster than a calculator Use the approximation 1 + kx to estimate t...
 3.11.19E: In Exercises 19–38, find dy.
 3.11.20E: In Exercises 19–38, find dy.
 3.11.21E: In Exercises 19–38, find dy.
 3.11.22E: In Exercises 19–38, find dy.
 3.11.23E: In Exercises 19–38, find dy.
 3.11.24E: In Exercises 19–38, find dy.
 3.11.25E: In Exercises 19–38, find dy.
 3.11.26E: In Exercises 19–38, find dy.
 3.11.27E: In Exercises 19–38, find dy.
 3.11.28E: In Exercises 19–38, find dy.
 3.11.29E: In Exercises 19–38, find dy.
 3.11.30E: In Exercises 19–38, find dy.
 3.11.31E: In Exercises 19–38, find dy.
 3.11.32E: In Exercises 19–38, find dy.
 3.11.33E: In Exercises 19–38, find dy.
 3.11.34E: In Exercises 19–38, find dy.
 3.11.35E: In Exercises 19–38, find dy.
 3.11.36E: In Exercises 19–38, find dy.
 3.11.37E: In Exercises 19–38, find dy.
 3.11.38E: In Exercises 19–38, find dy.
 3.11.39E: In Exercises 39–44, each function ƒ(x) changes value when x changes...
 3.11.40E: In Exercises 39–44, each function ƒ(x) changes value when x changes...
 3.11.41E: In Exercises 39–44, each function ƒ(x) changes value when x changes...
 3.11.42E: In Exercises 39–44, each function ƒ(x) changes value when x changes...
 3.11.43E: In Exercises 39–44, each function ƒ(x) changes value when x changes...
 3.11.44E: In Exercises 39–44, each function ƒ(x) changes value when x changes...
 3.11.45E: In Exercises 45–50, write a differential formula that estimates the...
 3.11.46E: In Exercises 45–50, write a differential formula that estimates the...
 3.11.47E: In Exercises 45–50, write a differential formula that estimates the...
 3.11.48E: In Exercises 45–50, write a differential formula that estimates the...
 3.11.49E: In Exercises 45–50, write a differential formula that estimates the...
 3.11.50E: In Exercises 45–50, write a differential formula that estimates the...
 3.11.51E: The radius of a circle is increased from 2.00 to 2.02 m.a. Estimate...
 3.11.52E: The diameter of a tree was 10 in. During the following year, the ci...
 3.11.53E: Estimating volume Estimate the volume of material in a cylindrical ...
 3.11.54E: Estimating height of a building A surveyor, standing 30 ft from the...
 3.11.55E: Tolerance The radius r of a circle is measured with an error of at ...
 3.11.56E: Tolerance The edge x of a cube is measured with an error of at most...
 3.11.57E: Tolerance The height and radius of a right circular cylinder are eq...
 3.11.58E: Tolerancea. About how accurately must the interior diameter of a 10...
 3.11.59E: The diameter of a sphere is measured as 100 ± 1 and the volume is c...
 3.11.60E: Estimate the allowable percentage error in measuring the diameter D...
 3.11.61E: The effect of flight maneuvers on the heart The amount of work done...
 3.11.62E: Measuring acceleration of gravity When the length L of a clock pend...
 3.11.63E: The linearization is the best linear approximation Suppose that y =...
 3.11.64E: Quadratic approximationsa. Let Q(x) = b0 + b1(x  a) + b2(x  a)2 b...
 3.11.65E: The linearization of 2xa. Find the linearization of ƒ(x) = 2x at x ...
 3.11.66E: The linearization of log3xa. Find the linearization of f(x) = log3x...
 3.11.67CE: In Exercises 67–72, use a CAS to estimate the magnitude of the erro...
 3.11.68CE: In Exercises 67–72, use a CAS to estimate the magnitude of the erro...
 3.11.69CE: In Exercises 67–72, use a CAS to estimate the magnitude of the erro...
 3.11.70CE: In Exercises 67–72, use a CAS to estimate the magnitude of the erro...
 3.11.71CE: In Exercises 67–72, use a CAS to estimate the magnitude of the erro...
 3.11.72CE: In Exercises 67–72, use a CAS to estimate the magnitude of the erro...
Solutions for Chapter 3.11: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321717399
Solutions for Chapter 3.11
Get Full SolutionsSince 71 problems in chapter 3.11 have been answered, more than 57604 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: University Calculus: Early Transcendentals , edition: 2. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.11 includes 71 full stepbystep solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321717399.

Binomial coefficients
The numbers in Pascal’s triangle: nCr = anrb = n!r!1n  r2!

Components of a vector
See Component form of a vector.

Compound fraction
A fractional expression in which the numerator or denominator may contain fractions

Coterminal angles
Two angles having the same initial side and the same terminal side

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

End behavior
The behavior of a graph of a function as.

Equal complex numbers
Complex numbers whose real parts are equal and whose imaginary parts are equal.

Factored form
The left side of u(v + w) = uv + uw.

Graph of a relation
The set of all points in the coordinate plane corresponding to the ordered pairs of the relation.

Graph of an inequality in x and y
The set of all points in the coordinate plane corresponding to the solutions x, y of the inequality.

Higherdegree polynomial function
A polynomial function whose degree is ? 3

kth term of a sequence
The kth expression in the sequence

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Parametric curve
The graph of parametric equations.

Perihelion
The closest point to the Sun in a planet’s orbit.

Period
See Periodic function.

Shrink of factor c
A transformation of a graph obtained by multiplying all the xcoordinates (horizontal shrink) by the constant 1/c or all of the ycoordinates (vertical shrink) by the constant c, 0 < c < 1.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

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

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.