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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
It cannot be determined without knowing the values of xand y
x − y > x − z
What property is shown by 4.0 x 5.0 does not equal 20.0?
It could be one of several things:
One is that the symbol "x" is used to indicate a binary operation other than conventional multiplication.
If multiplication IS in its "normal" form, it is possible that calculations are not in base 10. In base 7, for example, the answer would be 26.0
Or that calculations are modulo some number smaller than 20. Modulo 9, the answer would be 2.0
Or it could be the effect of rounding. For example 3.96 * 4.96 = 19.6416 so that rounded to 1 decimal place, this becomes 4.0 x 5.0 = 19.6 - not 20.0
It is very likely that there are other properties or scenarios.
Draw a straight line through the origin, slanting up at 45 degrees.
log(x6) = log(x) + log(6) = 0.7782*log(x)
log(x6) = 6*log(x)
What is the integral of the square root of 192x 100?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "equals", "squared", "cubed" etc.
There is no symbol before the 100.
What is the integral of one over the square root of forty-nine minus x squared?
Very sorry, I showed you how to take the derivative of the stated problem. I leave that below, however to take the integral you really just need your table of integrals.
The reference integral from my table (in my old calculus book) is:
integral of 1 / [ a2 - x^2]1/2 = sin-1|x / a| + c
a2 = 49 => a=7
x2 = x^2 => x = x
And your answer is:
sin
-1(x / 7) + c
If you are not allowed to use the table of integrals, the other alternative is trigonometric substitution.
Assume our integral is:
The integral of dx / sqrt ( a2 - x2)
Let x = a sin (θ)
dx = a cos (θ) d
θ
<-- this is just the derivative of x
θ = sin-1 (x/a) <-- solve the first equation for theta
So the integral transforms into:
the integral of ( a cos (θ)
d
θ
) / sqrt ( a2 -
a2sin2(θ) )
factor out an a2 in the root:
( a cos (θ)
d
θ
) / sqrt (
a
2 (1
-
sin2(θ) ) )
use the trig identity: sin2
(θ) + cos2
(θ) = 1
which can be rewritten:
1
-
sin2(θ) =
cos2
(θ)
and therefore:
( a cos (θ)
d
θ
) / sqrt (
a
2(
cos2
(θ)
) )
which simplifies to:
( a cos (θ)
d
θ
) /
( a cos (θ) )
which leaves us with the integral of
d
d
θ
it's now easy to solve and we get:
θ + C
plugin theta (from above):
sin
-1(x/a) + C
Plus in your a and x from the original equation, and you are good to go.
-----
Bonus: Here is how you find the derivative of this, since I already solved this on accident:
First, rewrite the expression to kill the fraction:1/(49-x2)1/2 =(49-x2)-1/2
Now, we can use u-substitution.
Let u = 49-x2
u` = -2x
Take thederivativeof u-1/2
(u-1/2)`= [ -u-3/2 ]/ 2
Now multiply by u`.
( [ -u-3/2]/ 2 ) ( -2x ) = (the 2's and negatives cancel)
x [ u-3/2] =
x / u3/2
Now plug u back in (remember: u = 49-x2)
x / u3/2 = x / (49-x2)3/2
The answer is:
x / (49-x2)3/2
How do you solve x squared plus 55 -2x equals 90?
x2 - 2x + 55 = 90
x2 - 2x - 35 = 0
(x+5)(x-7) = 0
x = -5, 7
How do you solve 2x 3y equals 11?
Unfortunately, limitations of the browser used by Answers.com means that we cannot see most symbols. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "equals".
There is no visible symbol between 2x and 3y.
Can you solve the equation 4x squared plus 7 equals 5?
Yes, but the solution is imaginary if you have learned that
4x^2 + 7 = 5
4x^2 = -2
x^2 = -1/2
x = +/-0.707i where i = square root of -1
What is x in this problem 2x 39.x?
Unfortunately, the browser used by Answers.com for posting questions is rubbish and incapable of accepting mathematical symbols. This means that we cannot see the mathematically critical parts of the question. We are, therefore unable to determine what exactly the question is about and so cannot give a proper answer to your question.
Why can you not divide a number by 0?
You can't divide something like 5 by nothing. It's irrational, because the number zero represents nothing, and that it is just a symbol recognizing that nothing is there. It's almost like an invisible thing, because 0 represents invisibility, because it is the only symbol justifying nothing in the numerical system.
