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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 are solutions for x to the second power plus 2x minus 8?
Factors are (x + 4)(x - 2) so x = -4 or 2
How can you solve this elimination x plus 8y equals 3 2x plus 3y equals -7?
x + 8y = 3 therefore 2x + 16y = 6 (a)
2x + 3y = -7 (b)
Subtract (b) from (a): 13y = 13 so y = 1 and x = -5
How do you tell where the input and output is on a function graph?
Normally the input is on the horizontal axis and the output on the vertical axis.
How do you solve 2x-1 times 3x plus 5 equals 5?
(2x-1)*(3x+5)=5
Use foil's method. First Outside Inside Last for multiplying
the equation turns out to this
(2x*3x)+(2x*5)+-(1*3x)+-(1*6)=5
Solve within the parentheses.
6x2+ 10x+-3x+-6=5
Continue to solve
6x2+7x+-6=5
You need to make =5 to =0
6x2+7x+-6+-5=5-5
6x2+7x+-11=0
quadratic formula is x=[-b +- {b^2*(-4ac)^2}]/2a
there are two equations to solve. the number and the opposite of a number
5b+6=32-8b
Since -8b contains the variable to solve for, move it to the left-hand side of the equation by adding 8b to both sides.
5b+6+8b=32
Since 5b and 8b are like terms, add 8b to 5b to get 13b.
13b+6=32
Since 6 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 6 from both sides.
13b=-6+32
Add 32 to -6 to get 26.
13b=26
Divide each term in the equation by 13.
(13b)/(13)=(26)/(13)
Simplify the left-hand side of the equation by canceling the common terms.
b=(26)/(13)
Simplify the right-hand side of the equation by simplifying each term.
b=2
What is the y intercept of 4x plus -3y equals -36?
I assume you mean.
4X - 3Y = -36
subtract 4X from each side
-3Y = -4X -36
divide both sides by -3
Y = 4/3X + 12
12 is Y intercept
What is the rate of change of the function y equal negative 5?
0. There is no x in your equation so regardless of how you change your input, the output y never changes.
How do you solve for x with equal values method?
First, if you have two equations like, for instance .90x+2000 and .40x+3500 then you would set them equal to each other like this ( .90x+2000=.40x+3500). Then you would solve for x by simplifying the equations as far down as you can.
What type of system is 3x plus 2y equals 7 and -4x-3y equals 10?
They are simultaneous equations and their solutions are x = 41 and y = -58
What is the antiderivative of radical 1 plus 3 radical x?
sqrt(1) + 3*sqrt(x) = 1 + 3*x^1/2So the antiderivative is x + [3*x^(3/2)]/(3/2) + c
= x + 2*x^(3/2) + c where c is the constant of integration.
What is the connection between anti-derivatives and definite integrals?
Definite integrals are definite because the limits of integration are prescribed. It is also the area enclosed by the curve and the ordinates corresponding to the two limits of integration. Antiderivatives are inverse functios of derivatives. If the limits of the integral are dropped then the integration gives antiderivative. Example Definite integral of x with respect to x between the value of x squared divided by 2 between the limits 0 and 1 is 1/2. Antiderivative of x is x squared divided by two.
Is f of x equal to negative x an even or odd function?
It is an odd function. Even functions use the y-axis like a mirror, and odd functions have half-circle rotational symmetry.
