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Calculus
The branch of mathematics that deals with the study of continuously changing quantities, with the use of limits and the differentiation and integration of functions of one or more variables, is called Calculus. Calculus analyzes aspects of change in processes or systems that can be modeled by functions. The English physicist, Isaac Newton, and the German mathematician, G. W. Leibniz, working independently, developed calculus during the 17th century.
25,068 Questions
What is discontinuity of a function?
continuty: for every point on a line, give me any distance no matter how small, within that distance of the point there is 2 other points ( or more) on the same function
discontinuty: does not satisfy that
How do you do 16 equals x plus 4.2?
you can subtract 4.2 from both sides of the equation.
16=x+4.2
(16)-4.2=(x+4.2)-4.2
11.8=x+4.2-4.2
11.8=x
What is the ordered pair for y equals -x-1?
y = -x-1 is an equation that defines y as a function of x. For each possible value of x, it tells us how to calculate the corresponding value of y. For example, when x is 3, y is -4. So the ordered pair (3, -4) belongs to the function. Similarly for other values of x. Some mathematicians define functions so that the ordered pair is the other way around, so that the above point would be written as (-4, 3). This is just an arbitrary notation convention. The important thing is to be consistent in whichever notation you use.
What is the center and radius of x2 plus 6x plus y2-6y-232 equals 0?
As I understood your question:
"What is the center and radius of: x2+6x+y2-6y-232=0?"
First move 232 over to the right hand side to get: x2+6x+y2-6y = 232.
Complete the square for both x's and y's: (x2 + 6x+ 9) + (y2 - 6y + 9) =232 + 9 + 9
Then rewrite: (x+3)2+(y-3)2=250
Now you can pick off the center --> (-3,3); and
radius --> sqrt(250) = 5sqrt(10) approx. 15.8114
What are some real life applications of a pattern in algebra?
Read word problems in a math book.
Joe pays 25 dollars for 3 cds. At the same rate, what should he pay for 105 cds?
What is the integral of 2x plus seven divided by x square plus 2x plus 5?
Hopefully I did this one correctly, if anyone sees an error please correct it. This is the problem:
∫(2x+7)/(x2+2x+5)
I rewrote the integral as:
2∫x/(x2+2x+5) + 7∫1/(x2+2x+5)
Both of these parts of the integral is in a form that should be listed in most integral tables in a calculus text book or on-line. From these tables the integral is the following:
2*[(1/2)ln|x2+2x+5| - (1/2)tan-1((2x+2)/4)] + 7*[(1/2)tan-1((2x+2)/4)]
Combining like terms gives the following:
ln|x2+2x+5| + (5/2)*tan-1((2x+2)/4)
What is the difference between gradient and vector notation?
In the name of God;
It must be mentioned that a vector has two important characteristics; 1- direction and 2- quantity. in other word for identification a vector these two characteristics must be defined. for example when we speak about displacement of a body it must has direction and quantity.
but about gradient, it has a general mean: difference.
Also a specified mean may be defined for it: "any increase or decrease in a vector or scalar field". it is a vector field.
What is the most popular approach to integration?
Legacy system integration. ...
Enterprise application integration (EAI) ...
Third-party system integration. ...
Business-to-business integration. ...
Point-to-point model. ...
Integration platform
What is the anti-derivative of sqrtx2-x?
f'(x) = (x2 - x)1/2
1. Add one to the exponent
2. Divide step 1 by the exponent plus one
= (x2 - x)1/2+1
____________
1/2 + 1
= (x2 - x)3/2
_________
3/2
= (2/3) (x2 - x)3/2 + C
It may also be written:
[2(x2 - x)3/2 / 3] + C
Check:
f(x) = (2/3) (x2 - x)3/2
Using the chain rule:
f'(x) = (2/3) (3/2) (x2 - x)3/2-1
= (x2 - x)1/2
Why does your low mile 2001 5.2 liter have half the power of your 1998 work truck with 300000 kms?
you have to consider weight. Is it the 1500-2500-3500? Size of tires? Size of wheels? If all these are the same you may want to check out your engine. Maybe your not running on all 8.
What is the next letter A f v u g l t?
If you read Ludwig Wittgenstein's comments on language games, you will find that any next-in-series problem has an infinite number of soluitons. I am curious, though, to learn what you or others think is the "uniquely correct" answer to your challenge.
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Can you write a program to generate sinx table where x varies from 0 to 180 in steps of 15?
Yes, I can.
6ms If C equals 22microfarad. what standard value must be used?
If an RC time constant of 6 ms is required and C= 22 ufd, then
R = (6 x 10-3) / (22 x 10-6) = 272.727 ohms (rounded)
The nearest EIA standard value for 2%, 5%, and 10% resistors is 270 Ω .
Yes, he was married to his fourth cousin, Louise de Long.
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