- 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
Addition principle of probability.
P(A or B) = P(A) + P(B) - P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)
Addition property of equality
If u = v and w = z , then u + w = v + z
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)
See Inverse cotangent function.
a + b = b + a ab = ba
Complex numbers a + bi and a - bi
See Right circular cone.
Future value of an annuity
The net amount of money returned from an annuity.
Horizontal shrink or stretch
See Shrink, stretch.
Imaginary part of a complex number
See Complex number.
A logarithm with base e.
Real numbers shown to the left of the origin on a number line.
Parametric equations for a line in space
The line through P0(x 0, y0, z 0) in the direction of the nonzero vector v = <a, b, c> has parametric equations x = x 0 + at, y = y 0 + bt, z = z0 + ct.
Reduced row echelon form
A matrix in row echelon form with every column that has a leading 1 having 0’s in all other positions.
A triangle with a 90° angle.
Set of all possible outcomes of an experiment.
Solution of a system in two variables
An ordered pair of real numbers that satisfies all of the equations or inequalities in the system
Solve a system
To find all solutions of a system.
Standard form of a polynomial function
ƒ(x) = an x n + an-1x n-1 + Á + a1x + a0
A point that lies on both the graph and the y-axis.
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