What is Calculus ii: Definition and 107 Discussions
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
It has two major branches, differential calculus and integral calculus; the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves. These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. Today, calculus has widespread uses in science, engineering, and economics.In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. The word calculus (plural calculi) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine – see Calculus (medicine)). Because such pebbles were used for counting (or measuring) a distance travelled by transportation devices in use in ancient Rome, the meaning of the word has evolved and today usually means a method of computation. It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus.
"Work" (Calculus II)
This is a problem from the chapter called "Work":
A water tank in the form of an inverted right-circular cone is 29 ft across the top and 15 ft deep. If the surface of the water is 5 ft. below the top tank, find the work done in pumping the water to the top of the tank...
The problem:
(\int f(x)dx)(\int \frac{1}{f(x)} dx) = -1
solve for f(x)
The attempt at a solution
divide both sides by integral(f(x)dx):
\int \frac{1}{f(x)} dx = \frac{-1}{\int f(x)dx}
took derivative of both sides:
\frac{1}{f(x)} = \frac{f(x)}{(\int f(x) dx)^2}
multiplied both sides by f(x)...
Calculus II homework help...
Hi,
I am new to this forum and I found about this forum on talk.collegeconfidential.com. Well I have been having some trouble with my Calc II work . It would be great if someone could explain this problem to be
Find the total length of the astroid x=a (cos...
Calculus II is giving me a hard time!
Im embarrased to say this but I've taken Cal II 2 times already and can't get passed it. I don't understand what I am doing wrong. I am taking it this summer for the sake of getting it all over with quickly. I was confident when I went into class because I...
What test can I use on the following series in order to determine
if it converges or diverges? Looking at it graphically it appears to
diverge but I cannot show it analytically.
\sum\limits_{n = 1}^\infty {\frac{{n!}}{{3n! - 1}}}
Using the Ratio Test, here is I got thus far
\left|...
Hi. I need help on how to set up the integral for these problems.
1. A cylindrical gasoline tank is placed so that the axis of the cylinder is horizontal. Find the fluid force on a circular end of the tank if the tank is half full, assuming that the diameter is 3 feet and the gasoline...
The Deligne Dam on the Cayley River is built so that the wall facing the water is shaped like the region above the curve y=0.6 x^2 and below the line y= 164 . (Here, distances are measured in meters.) The water level can be assumed to be at the top of the dam. Find the force (in Newtons) exerted...