- 13.AAE.1AAE: Function with saddle at the origin If you did Exercise 60 in Sectio...
- 13.AAE.2AAE: Finding a function from second partials Find a function w=f(x,y) wh...
- 13.AAE.3AAE: A proof of Leibniz’s Rule Leibniz’s Rule says that if ƒ is continuo...
- 13.AAE.4AAE: Finding a function with constrained second partials Suppose that ƒ ...
- 13.AAE.5AAE: Homogeneous functions A function ƒ(x, y) is homogeneous ofdegree n ...
- 13.AAE.6AAE: Surface in polar coordinates Let where r and theta are polar coordi...
- 13.AAE.7AAE: Properties of position vectors
- 13.AAE.8AAE: Gradient orthogonal to tangent Suppose that a differentiable functi...
- 13.AAE.9AAE: Curve tangent to a surface Show that the curve is tangent to the su...
- 13.AAE.10AAE: Curve tangent to a surface Show that the curve
- 13.AAE.11AAE: Extrema on a surface Show that the only possible maxima and minima ...
- 13.AAE.12AAE: Maximum in closed first quadrant Find the maximum value of in the c...
- 13.AAE.13AAE: Minimum volume cut from first octant Find the minimum volume for a ...
- 13.AAE.14AAE: Minimum distance from a line to a parabola in xy -plane By minimizi...
- 13.AAE.15AAE: Boundedness of first partials implies continuity Prove the followin...
- 13.AAE.16AAE: Suppose that is a smooth curve in the domain of a differentiable fu...
- 13.AAE.17AAE: Finding functions from partial derivatives Suppose that ƒ and g are...
- 13.AAE.18AAE: Rate of change of the rate of change We know that if ƒ(x, y) is a f...
- 13.AAE.19AAE: Path of a heat-seeking particle A heat-seeking particle has the pro...
- 13.AAE.20AAE: Velocity after a ricochet A particle traveling in a straight line w...
- 13.AAE.21AAE: Directional derivatives tangent to a surface Let S be the surface t...
- 13.AAE.22AAE: Drilling another borehole On a flat surface of land, geologists dri...
- 13.AAE.23AAE: Find all solutions of the one-dimensional heat equation of the form...
- 13.AAE.24AAE: Find all solutions of the one-dimensional heat equation that have t...
Solutions for Chapter 13.AAE: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
An interval that has finite length (does not extend to ? or -?)
equation of an ellipse
(x - h2) a2 + (y - k)2 b2 = 1 or (y - k)2 a2 + (x - h)2 b2 = 1
An equation written with exponents instead of logarithms.
A method of solving a system of n linear equations in n unknowns.
General form (of a line)
Ax + By + C = 0, where A and B are not both zero.
Connected subset of the real number line with at least two points, p. 4.
Inverse secant function
The function y = sec-1 x
Jump discontinuity at x a
limx:a - ƒ1x2 and limx:a + ƒ1x2 exist but are not equal
The final digit of a number in a stemplot.
A graph of a polar equation of the form r2 = a2 sin 2u or r 2 = a2 cos 2u.
Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.
Real numbers shown to the right of the origin on a number line.
An expression that can be written as a ratio of two polynomials.
The difference y1 - (ax 1 + b), where (x1, y1)is a point in a scatter plot and y = ax + b is a line that fits the set of data.
A real number.
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.
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.
The square of the standard deviation.