0
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
They can be any values in the domain of the function.
x3 + 7x = 8x2
x3 + 7x - 8x2 = 0 [subtract 8x2 from both sides]
x(x2 + 7 - 8x) = 0 [factor out x]
x(x-1)(x-7) = 0 [factor]
Since the product of the three factors x, x-1, and x-7 equals zero, any of the three expressions could equal zero:
x = 0
x - 1 = 0, x = 1
x - 7 = 0, x = 7
Therefore, there are three solutions to the equation x3 + 7x = 8x2:
- x = 0
- x = 1
- x = 7
Or, in set notation: x = {0,1,7}
What does the equation y equals x2 - 6x plus 2 become after completing the square?
y = x2 - 6x + 2
y = x2 - 6x + 9 - 7
y = (x - 3)2 - 7
F the expression 2x plus 6 equals 20 what is the value of x?
Subtract 6 from each side: 2x = 14; divide each side by 2: x = 7
How do you factor e raised to 2x -1 divided by e raised to x minus 1?
This question involves a property of dividing common bases. For example, xm/xn is the same as saying x(m-n). Whenever two common bases are being divided, the exponents can be combined by subtraction.
So, for this problem: e(2x-1)/e(x-1), the e can be written once, with the exponents being subtracted:
e2x-1-(x-1), distributing the minus sign arrives at e2x-1-x+1, or ex.
ANS: ex
What is the indefinite integral?
An indefinite integral is a version of an integral that, unlike a definite integral, returns an expression instead of a number.
The general form of a definite integral is:
∫ba f(x) dx.
The general form of an indefinite integral is:
∫ f(x) dx.
An example of a definite integral is:
∫20 x2 dx.
An example of an indefinite integral is:
∫ x2 dx
In the definite case, the answer is 23/3 - 03/3 = 8/3.
In the indefinite case, the answer is x3/3 + C, where C is an arbitrary constant.
Solve -3x plus 4 equals 2x plus 24?
Add 3x to each side: 4 = 5x + 24
Subtract 24 from each side: -20 = 5x
Divide each side by 5: -4 = x
In calculus what is the power rule?
I've heard what I'm going to tell you called the "power rule" before. It's the only thing I've ever heard referred to as the power rule.
It's simply the way to find the derivative of a polynomial function, something of the form:
y=axn
where a and n are any real number
The power rule states that to find the derivative (y-prime (y')) of any function of this type, you simply follow this format:
y'=an*xn-1
following this format to higher derivatives:
y''=(a)(n)(n-1)xn-2
y'''=(a)(n)(n-1)(n-2)xn-3
In written terms, you simply bring down the current exponent in front of the variable and lower the exponent by one to make the derivative.
For three examples:
y=6x3
y'=(6)(3)x3-1=18x2
y''=(18)(2)x2-1=36x1=36x
y'''=(36)(1)x1-1=36x0=36
y=7x-3=7/x3
y'=(7)(-3)x-3-1=-21x-4
and so on...
y=4sqrt(x)=4x1/2
y'=(4)(1/2)x(1/2)-1=2x-1/2
and so on...
The last two examples were to show that this method still works for negative exponents, fractional exponents...any exponent that is a real number.
This does not apply only to functions who are purely polynomial. Any component of a larger function that is polynomial can be derived in this way (as long as the component is added or subtracted; division or subtraction brings the product rule into play).
For example:
y=2x2+cos(x-2)
The component "2x2" has a derivative of 4x due to the power rule.
For the record:
y'=4x-sin(x-2)
How to calculate the period of a simple harmonic motion?
by using the formula we will calculat time period of simple harmonic motion
If x plus y equals 7 and y equals 5 then x plus 5 equals 7?
Yes.
This is a logical deduction based on substitution.
if x + y = 7 and y = 5 then the value of 5 can be substituted for y to get x + 5 = 7 which can then be solved to get x = 2, meaning the point (2, 5) is a solution to the line x + y = 7 as it is on that line.
How do you solve 3x plus 2y equals 4 4x plus 3y equals 7?
You need to organise your question properly.
3x+2y=4 4x + 3y= 7?
Is 4 4x = 44x or 4-4x or 4+4x
How can there be 2 equal signs in 1 equation?
What describes the graph of gx equals -3x plus 5?
A straight line, passing through the point (0,5) with a gradient of -3.
How many real solutions are there in the equation 2x2 plus 2x - 4 equals 0?
0 = 2x^2 + 2x - 4 = 2(x^2 + x - 2) = 2(x-1)(x+2)
Thus, there are two real solutions:
x = 1 and x = -2
What is x squared plus 8x minus 20 equals 0 if you solve by factoring show work?
x2 + 8x - 20 = 0
(x + 10) (x - 2) = 0
(x+10) = 0 . . . . . x = -10
(x - 2) = 0 . . . . . x = 2
Please be sure to copy the work accurately before you hand it in. If you were to
hand it in with a stupid blunder, it could affect our reputation as a reliable place
to go to have other people do your homework for you.
Are y equals 2x plus 5 Parallel yes or no?
If they have the same slope or gradient of 2 but different y intercepts then they are parallel.
You have not given enough information for a yes or no answer.
What test determines if a function is one to one?
First recall that a function is one to one if no two elements in its domain have the same element in the range
One trick to finding out if a function is one to one is to use the Horizontal line test. You may view the link for a better explanation.
The main idea is if a horizontal line intersects the graph of a function more than one time, then the function is not one to one. This is important because if it is not one to one, it has no inverse.
