Calculus

A lot of people think of a function as an "equation," but it can be more general than that. In formal definitions, a function is a "rule" that assigns every input to exactly one output. You might see a function as a graph, an equation, a table, or an obnoxious person that shouts back at you every word you say, but in pig latin.

The limit of a function exists if, as the input x approaches something, the output f(x) approaches something--regardless of the output when x actually reaches the thing it approaches. The limit is the thing that f(x) approaches. For example, picture (or Google), the graph of f(x) = 1/x. As x approaches infinity (further and further to the right of the graph), the curve f(x) gets closer and closer to the x-axis--meaning it gets closer and closer to zero.

Call your local UPS or Postal Service and ask. Rather be safe than sorry.

It is a cubic equation in the variable x.

5

(13x^2 - 4y)(2x^2 - 5y)

6

use the line equation y=mx+b

plug in the slope (rise over run) 4/1

y=4x+b

plug in the y intercept (4)

y=4x+4

29 x 527 = 15283.

0

x2 + x = 1 - x

So x2 + 2x - 1 = 0

Using the quadratic formula,

x = {-2 ± sqrt[22 - 4*1*(-1)]}/(2*1)

= -1 ± sqrt(2)

51.3+1.3 = 52.6

d/dt (7s/2t3) = negative 21s/2t4 (ds/dt)


(Not bad for stuff I haven't used in 30 years, eh ?)

The derivative of any expression is the rate at which it changes. A constant, such as

a number made from digits, doesn't change, so its derivative is zero.

485 is a constant. It doesn't change, so its derivative (the rate at which it changes)

is zero.

You can also take any constant, call it c, and apply the definition of a derivative using limits. Lim as h goes to 0 of {f(x+h)-f(x)}/h becomes lim as h goes to 0 of (c-c)/h which is 0

3x2 + 4x - 15 = 0, solve by using the quadratic formula.

a = 3, b = 4, c = -15

x = [-b ± √(b2 - 4ac)]/(2a)

x = [-4 ± √(42 - 4*3*-15)]/(2*3) = [-4 ± √(16 + 180)]/6 = (-4 ± √(196)/6 = (-4 ± 17)/6

x = (-4 +17)/6 = 13/6 or x = (-4 - 17)/6 = -21/6 = -7/2

The solution set: {-7/2, 13/6}.

In the 'real world', the purpose of a course of study in pre-calculus

is to prepare the student for a course of study in Calculus.

About 35.3147 cubic feet or 4.1923 Hogshead.

328.1 feet.

The next number in the series will be 66. The next number is found by adding the two previous numbers. (2+7=9, 9+7=16, etc...)

D'Alembert's ratio test, or simply the ratio test, is a way of determining whether certain series converge. It goes like this: to check if a series converges, check the sequence of ratios between consecutive terms. If that sequence converges to something less than 1, then the series converges absolutely. If it converges to something greater than 1, or diverges, then the series diverges. If it converges to 1 exactly, then the test is inconclusive.

There are 25.4 millimetres in one inch. Therefore, rounded to three significant figures, 7 inches is equal to 7/25.4 = 0.276 inches.

Direct Conversion Formula 7 mm*

1 in

25.4 mm

=

0.2755905512 in

6

X equals any number you wish.

For example, if x=1, then 1(2)+1 equals 3

1.25 gallons.