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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 x to the 2nd equals 9 over 16?
x2 = 9/16
It's a second-degree equation in 'x'.
The solutions are:
x = positive 3/4 .
x = negative 3/4 .
x2 + x = 1 - x
So x2 + 2x - 1 = 0
Using the quadratic formula,
x = {-2 ± sqrt[22 - 4*1*(-1)]}/(2*1)
= -1 ± sqrt(2)
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'.
