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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
How much is 18 equals 3 plus 5x for x?
Your question is actually: "What is 'x' if [18 = 3 + 5x] ?"
18 = 3 + 5x
Subtract 3 from each side of the equation:
15 = 5x
Divide each side by 5:
3 = x
What happens to y as x moves towards negative infinity?
The value of y as x changes depends on the function under consideration. The answer could be any of the following (or something quite different):
- y approaches a specific value
- y approaches positive or negative infinity
- y is undefined
What is the pH of a solution with a H plus equals 1.4 x 10-3 M?
-Log(1.4x10-3)= 2.85
The Log to be used here is the decimal one, not the neperian one.
When can you say that the graph is function or mere relation?
If a vertical line intersects the graph at more than one point then it is not a function.
How do you solve 4x plus 8y raised to the second?
The first thing you have to do is make sure you understand the question,
and know what it's looking for as a solution. You're not there yet.
Equations have solutions, but this is not an equation. It's an expression that
stands for a number. There's no way to figure out what the number is until
somebody tells you what numbers 'x' and 'y' are.
There's no question in your question, and nothing that needs to be solved.
How long does it take to count to a million?
Naturally, that depends on how fast you can count.
But if you can count from 1 to 100 in one minute, and you keep counting every minute, without stopping, for eight hours every day (taking time off to eat, sleep, and go to school), you would reach 1,000,000 in 20 days, 6 hours, and 40 minutes, or almost 3 weeks.
If, however, you give up eating, sleeping, and school, and just count every minute of every hour of every day, you would reach 1,000,000 in 6 days, 22 hours, and 40 minutes, almost 1 week.
What is the highest number ever counted?
Well, for my part, I just recently counted past (decimal) "one and a half million" ("1,519,616" to be "exact"), and am still counting (and I have relied very little on writing down where I am as I count). I am actually counting (at present) in a base that I could be called "balanced base-sixty-four" or "quadrosexagesimal"; and - in that base - the number would be "6¯d00". In "base thirty-two" or "duotrigesimal", it would be "1ec00". I started this particular counting project about a year and a half ago now, and - God willing - will keep counting at least until I reach (decimal) 33,554,432 - which is "1,00000" in duotrigesimal or "20000" in quadrosexagesimal.
(By the way the over-bar "¯" indicates a negative rather than positive value, the symbols "c", "d", and "e" represent decimal "12", "13", and "14" respectively. So, for example, "¯d" represents decimal: "negative 13". Also, in base sixty-four and base thirty-two, each "place" to the left represents a power of decimal "64" and "32", respectively. Therefore, thequadrosexagesimal value: " 6 ¯d 0 0 " equals decimal 6*64^3 - 13*64^2; and the duotrigesimal: " 1 e c 0 0 " equal decimal 1*32^4 + 14*32^3 + 12*32^2. Furthermore, quadrosexagesimal "20000" equals 2*64^4 and duotrigesimal "1,00000" equals 32^5.)
Give a one-line C expression to test whether a number is a power of 2?
The one line expression is:
((0 != n) && !(n & n-1))
example:
int main ()
{
for (int n = 0; n <= 1000001; ++n)
{
if ((0 != n) && !(n & n-1))
cout << n << " is a power of 2" << endl;
}
return 0;
}
will produce:
1 is a power of 2
2 is a power of 2
4 is a power of 2
8 is a power of 2
16 is a power of 2
32 is a power of 2
64 is a power of 2
128 is a power of 2
256 is a power of 2
512 is a power of 2
1024 is a power of 2
2048 is a power of 2
4096 is a power of 2
8192 is a power of 2
16384 is a power of 2
32768 is a power of 2
65536 is a power of 2
131072 is a power of 2
262144 is a power of 2
524288 is a power of 2
How do you find out the domain of x squared?
You can square any real number (complex ones too) so the domain is all real numbers.
Is 3x plus 2y equals 3 in function form?
A more conventional functional form would be y = (3 - 2x)/2. I am not sure that there is any generally recognized limit on how functions can be expressed
9x6x5=270 cubic millimeters.
1000 cubic millimeters is a cubic centimeter
What is the Taylor Series of f of x equals x squared minus x cubed centered at a equals 2?
f(x)=x2-x3
f(2) = 4-8 = -4
f'(x) =2x-3x2
f'(2) = 4-12=-8
f''(x) = 2 -6x
f''(2)= -10
f'''(x)= -6
f(n)(x) = 0 for all n > 3.
f(x) = f(2) + (x-2) f'(2) / 1! + (x-2)2 f''(2) /2! + (x-2)3 f'''(2)/3! + . . .
f(x) = -4 -8(x-2) -10(x-2)22/2-6(x-2)3/6 + 0 + 0 + ...
f(x) = -4 -8(x-2) -5(x-2)2 - (x-2)3
This is a parabola pointing 'down'. It's apex is at the point (4,0). It crosses the x-axis at the points (2,0) and (-2,0)
y=-x-4
as this is in the form of y=mx+b, the slope of this line is -1.
5x + 5y = 20
x + y = 4
y = -x + 4
the slope of this line is -1.
Since the slope of each of the two lines are the same (-1) they are in fact parallel to each other, not perpendicular.
How do you solve log x plus 2 equals log 9?
log x + 2 = log 9
log x - log 9 = -2
log (x/9) = -2
x/9 = 10^(-2)
x/9 = 1/10^2
x/9 = 1/100
x= 9/100
x=.09
What is the integral of rootsquare 1 plus x2 over x without using partial fraction?
Int sqrt(1+x2)/x = sqrt(1+x2) + LN [(sqrt(1+x2) - x -1) / (sqrt(1+x2) - x +1)]
