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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 derivative of lnx raised to 4?
ln(x4)?
d/dx(ln(u))=1/u*d/dx(u)
d/dx(ln(x4))=[1/x4]*d/dx(x4)
-The derivative of x4 is:
d/dx(x4)=4x4-1
d/dx(x4)=4x3
d/dx(ln(x4))=[1/x4]*(4x3)
d/dx(ln(x4))=4x3/x4
d/dx(ln(x4))=4/x
(lnx)4?
Chain rule: d/dx(ux)=x(u)x-1*d/dx(u)
d/dx(lnx)4=4(lnx)4-1*d/dx(lnx)
d/dx(lnx)4=4(lnx)3*d/dx(lnx)
-The derivative of lnx is:
d/dx(ln(u))=1/u*d/dx(u)
d/dx(lnx)=1/x*d/dx(x)
d/dx(lnx)=1/x*(1)
d/dx(lnx)=1/x
d/dx(lnx)4=4(lnx)3*(1/x)
d/dx(lnx)4=4(lnx)3/x
What is true 15 plus 0 equals 0 15-0 equals 0 15 percent 0 equals 0 0 percent 15 equals 0?
15 percent 0 equals 0;
0 percent 15 equals 0.
Both the above are true
Which length of the pendulum made the most number of swings?
A shorter pendulum will make more swings per second. Or per minute. Or whatever.
How would you prove algebraically that the function f(x) x-2 x 2 is one to one?
How would you prove algebraically that the function: f(x)= |x-2|, x<= 2 , is one to one?
What is the solution set to the equation x2 plus 4 equals 0?
There are no real solutions to this equation because you cannot take the square root of a negative number. However,
x2 + 4 = 0
x2 = -4
sqrt(x2) = sqrt(-4)
x = 2i, -2i
here are the imaginary solutions.
What ist the formula fir velocity?
The formula for velocity is (v = d/t) or (velocity = distance/time).
Is it possible for a function that has a horizontal asymptote to attain the value of an asymptote?
Yes.
Think of a function that starts at the origin, increases rapidly at first and then decays gradually to an asymptotic value of 0. It will have attained its asymptotic value at the start.
For example, the Fisher F distribution, which is often used, in statistics, to test the significance of regression coefficients. Follow the link for more on the F distribution.
How do you figure out decimals?
the number devided by 100, 9 devided by 100 is 0.009, i think lol
one half = 0.5 in decimals, decimals relaate to fractions a lot, if u still dont get me, go onto youtube and type in your question and my videos will come up, i make them with friends.
How many combinations can you make with four ingredients?
24, You can use permutations on a calculator or on paper to solve questions like these.
Ex.
Permutation: 4! = 4 x 3 x 2 x 1 = 24
What is the square root of x plus 2 plus square root of x plus 3?
That expression can't be simplified. It has to written,
and evaluated, just as it appears in the question:
[ sqrt(x + 2) ] + [ sqrt(x + 3) ]
What is the focus and directrix of y equals 8x squared?
Need set of point parabola passes through.
X = 1
Y = 8
----------------(1, 8)
For focus,
X2 = 4pY
insert values, solve for p
(1)2 = 4p(8)
= 1/32
=======focus
- 1/32
=======directrix
( long time since I have done this. Formula is correct, check my math )
How do you differentiate and find the tangent?
When you differentiate a function, you find the slope of the function. The slope is also known as the tangent.
The slope of a line, given one point, and a second point relative to the first point, but with x different, is given as delta y over delta x.
Differentiation is simply taking the limit of the slope, i.e. where delta x approaches zero.
3x plus 5y equals 1 2x plus 3y equals 1?
I assume you are trying to find the values of both x and y.
3x+5y=1
2x+3y=1
Since both equal 1 we can set them equal to each other.
3x+5y=2x+3y
Now, we want to get all the x's on one side and all the y's on the other side.
Subtract 2x from both sides and subtract 5y from both sides to isolate x's and y's
This will result in x=(-2y)
Since we now know X in terms of Y we can plug the value into one of the original equations.
Lets use 2x+3y=1. x=(-2y) So, 2(-2y)+3y=1 or -4y+3y=1 y=-1
Plugging in the value of y to the other equations will give us the value of x.
2x+3(-1)=1 so (2x-3=1) Solving this results in x=2
To double check lets put both values into the first equation to see if it works.
3(2)+5(-1)=1 6-5=1.
It works so we are now certain that y=(-1) and x=2
Let f x equals x2 plus 5x plus 3 Find f 2?
If I understand this right...
f(x) = x2 + 5x + 2
f(x) is a function, in this case a function of x. Using this function, you can say...
f(g) = g2 + 5g + 2
f(pi) = pi2 + 5pi + 2
All we're doing is substituting whatever's in the brackets on the other side. Thus...
f(2) = 22 + 5*2 + 2
