- 7.AAE.1AAE: Let A(t) be the area of the region in the first quadrant enclosed b...
- 7.AAE.2AAE: Varying a logarithm’s basea.Find b. Graph y = loga 2 as a function ...
- 7.AAE.3AAE: Graph f(x) = tan-1 x + tan-1(1/x) for . Then use calculus to explai...
- 7.AAE.4AAE: Graph f(x) = (sin x)sin x over [0, 3?]. Explain what you see.
- 7.AAE.5AAE: Even-odd decompositionsa. Suppose that g is an even function of x a...
- 7.AAE.6AAE: Let g be a function that is differentiable throughout an open inter...
- 7.AAE.7AAE: Center of mass Find the center of mass of a thin plate of constant ...
- 7.AAE.8AAE: Solid of revolution The region between the curve and the x-axis fro...
- 7.AAE.9AAE: The Rule of 70 If you use the approximation (in place of 0.69314 . ...
- 7.AAE.10AAE: Urban gardening A vegetable garden 50 ft wide is to be grown betwee...
Solutions for Chapter 7.AAE: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
Continuous at x = a
lim x:a x a ƒ(x) = ƒ(a)
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment
Factoring (a polynomial)
Writing a polynomial as a product of two or more polynomial factors.
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.
y = b.
See Mathematical induction.
Connected subset of the real number line with at least two points, p. 4.
One-to-one rule of exponents
x = y if and only if bx = by.
See Periodic function.
Permutations of n objects taken r at a time
There are nPr = n!1n - r2! such permutations
Quadratic equation in x
An equation that can be written in the form ax 2 + bx + c = 01a ? 02
The formula x = -b 2b2 - 4ac2a used to solve ax 2 + bx + c = 0.
The measure of a central angle whose intercepted arc has a length equal to the circle’s radius.
Two points that are symmetric with respect to a lineor a point.
Reflection across the y-axis
x, y and (-x,y) are reflections of each other across the y-axis.
Shrink of factor c
A transformation of a graph obtained by multiplying all the x-coordinates (horizontal shrink) by the constant 1/c or all of the y-coordinates (vertical shrink) by the constant c, 0 < c < 1.
Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,
Sum of a finite geometric series
Sn = a111 - r n 2 1 - r
Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.
The points x, y, 0 in Cartesian space.