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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 the dy over dt of y equals 7s over 2t3?
d/dt (7s/2t3) = negative 21s/2t4 (ds/dt)
(Not bad for stuff I haven't used in 30 years, eh ?)
What is the derivative of 485?
The derivative of any expression is the rate at which it changes. A constant, such as
a number made from digits, doesn't change, so its derivative is zero.
485 is a constant. It doesn't change, so its derivative (the rate at which it changes)
is zero.
You can also take any constant, call it c, and apply the definition of a derivative using limits. Lim as h goes to 0 of {f(x+h)-f(x)}/h becomes lim as h goes to 0 of (c-c)/h which is 0
What is the solution set for 3x2 plus 4x 15 equals 0?
3x2 + 4x - 15 = 0, solve by using the quadratic formula.
a = 3, b = 4, c = -15
x = [-b ± √(b2 - 4ac)]/(2a)
x = [-4 ± √(42 - 4*3*-15)]/(2*3) = [-4 ± √(16 + 180)]/6 = (-4 ± √(196)/6 = (-4 ± 17)/6
x = (-4 +17)/6 = 13/6 or x = (-4 - 17)/6 = -21/6 = -7/2
The solution set: {-7/2, 13/6}.
Is every function a onto function?
No. It depends on how the range is defined.
y = x2 is not onto R but can be made onto by changing the range to R0+.
No. It depends on how the range is defined.
y = x2 is not onto R but can be made onto by changing the range to R0+.
No. It depends on how the range is defined.
y = x2 is not onto R but can be made onto by changing the range to R0+.
No. It depends on how the range is defined.
y = x2 is not onto R but can be made onto by changing the range to R0+.
How is calculus used in the real world?
In the 'real world', the purpose of a course of study in pre-calculus
is to prepare the student for a course of study in Calculus.
Which is going to be the next number in the line 2 7 9 16 25 41?
The next number in the series will be 66. The next number is found by adding the two previous numbers. (2+7=9, 9+7=16, etc...)
What is D'Alembert's ratio test?
D'Alembert's ratio test, or simply the ratio test, is a way of determining whether certain series converge. It goes like this: to check if a series converges, check the sequence of ratios between consecutive terms. If that sequence converges to something less than 1, then the series converges absolutely. If it converges to something greater than 1, or diverges, then the series diverges. If it converges to 1 exactly, then the test is inconclusive.
How many inches are there in 7 millimetres?
There are 25.4 millimetres in one inch. Therefore, rounded to three significant figures, 7 inches is equal to 7/25.4 = 0.276 inches.
Direct Conversion Formula 7 mm*
1 in
25.4 mm
=
0.2755905512 in
What is the value of x 2 plus x?
X equals any number you wish.
For example, if x=1, then 1(2)+1 equals 3
What is the derivative of 2 to the power of 5x?
25x?
d/dx(au)=au*ln(a)*d/dx(u)
d/dx(25x)=25x*ln(2)*d/dx(5x)
-The derivative of 5x is:
d/dx(cu)=c*du/dx where c is a constant
d/dx(5x)=5*d/dx(x)
d/dx(25x)=95x*ln(2)*(5*d/dx(x))
-The derivative of x is:
d/dx(x)=1x1-1
d/dx(x)=1*x0
d/dx(x)=1*(1)
d/dx(x)=1
d/dx(25x)=25x*ln(2)*(5*1)
d/dx(25x)=25x*ln(2)*(5)
-25x can simplify to (25)x, which equals 32x.
d/dx(95x)=32x*ln(2)*(5)
Given:
a = 2πr2 + 2πrh
h = 113/r2
∴ a = 2πr2 + 2πr(113/r2)
∴ a = 2πr2 + 226π / r
∴ da/dr = 4πr + 226π ln r
-13.9x equals 5.7-12.5x what is x equal to?
-13.9x = 5.7-12.5x ( +12.5x)
-1.4x = 5.7 (/-1.4)
x = 5.7/-1.4 = -4.07 to 2 decimal points
How would you solve 6xn plus 7y equals -6 -2x-3y equals 2 using addition method?
6x+7y=-6 3(-2x-3y=2)
+________
-2y=0 => y=0
Therefore x=-1
What is the solution of 4x plus 3y equals -12?
A solution means: Show the numerical values of 'x' and 'y'.
You can't find either one with only a single equation. You need another one.
When you have two equations, you can find values for both 'x' and 'y'.
Provide at least three coordinates to graph the equation 2x plus 3y equals 15 Show your work?
Plug in various values of x and solve for y. [This can be done for any value of x.]
For example, for x=0,
2*0+3y=15
3y=15
y=15/3=5
So (0,5) is one coordinate.
For x=1,
2*1+3y=15
2+3y=15
3y=13
y=13/3
So (1,13/3) is another coordinate.
For x=2,
2*2+3y=15
4+3y=15
3y=11
y=11/3
So (2,11/3) is another coordinate.
Solve the equation cos x root y equals 5 solve for y and differentiate to get y prime in terms of x?
cosx√y=5
Right away you can tell that there'll be a domain error because if you were to take cosine inverse five equals X root y then there would be an error
27, 54, 81, 108, 135, 162, 189, 216, 243, 270, 297, 324, 351, 378, 405, 432, 459, 486, 513, 540, 567, 594, 621, 648, 675 . . . ∞
What is the answer to x2 plus 8x plus 12 equals?
There is no single value that this equals. There could be any number of answers to it depending on the value of x.
If you want to know what x equals when a specific value is assigned to the equation, you can do this by solving the equation for a 0 value, and then factoring the result.
For example, let's say you you want to know the value of x when the equation equals negative four:
x2 + 8x + 12 = -4
∴ x2 + 8x + 16 = 0
∴ (x + 4)2 = 0
Now you simply plug in the value on the left side of the equation that would give you a result of 0. In this case, it would be negative four, as negative 4 plus 4 equals 0, which is also 0 when squared.
∴ x = -4
Similarly, if you say that the equation comes to a value of 5:
x2 + 8x + 12 = 5
∴ x2 + 8x +7 = 0
∴ (x + 7)(x + 1) = 0
In this case, there are two possible outcomes: negative 7 and negative 1. That's because either one of those will produce a zero value for this equation.
∴ x = -7 or x = -1
Alternately, what happens if the equation comes to a value of 1?
x2 + 8x + 12 = 1
∴x2 + 8x + 11 = 0
In this case, there is no simple way to solve it by factoring, so instead you can plug it into the quadratic formula, x = [-b +/- √(b2 - 4ac)] / 2a
∴ x = [-8 +/- √(82 - 4×1×11)] / (2×1)
∴ x = [-8 +/- √(64 - 44)] / 2
∴ x = (-8 +/- √20) / 2
∴ x = -4+√20, or -4-√20
∴ x ≈ 0.47214, or x ≈ -8.42714
As shown, there can be any number of correct answers to this, as there is no specified value for x. Once a value is specified, then it will always have at most two answers, and at least one.
