Is that normal?1 AnswerOther - Health9 years ago
I know that you can differentiate integrals to prove that they are the correct integral.
I'm not really sure how to differentiate a by parts integral though.
This was the question:
Evaluate the integral using the indicated choice of u and dv.
integrate ( [x^2]*ln(x))dx
when u=lnx and dv=x^2dx
My answer was:
1/3(x^3)ln(x)-1/9(x^3) + c
Now I want to prove this is the right answer by differentiation.
How? Can someone explain to me how this is possible IN GENERAL (not necessarily just for this question), please?
I have absolutely no idea how to do this, in class we didn't go over how to implicitly differentiate ellipses very much.
Use implicit differentiation to find an equation of the tangent line to the curve at the given point.
x^2 + xy + y^2 =3 , (ellipse)
Please explain how you did this!3 AnswersMathematics9 years ago
What is the instantaneous speed of the object at the instant of impact?
Using this equation:
Would I find the total time it was falling, then plug that total time into the equation and get the height, then put the height where h(t) is, and then solve for t?
I'm not sure. I'm trying to review. Please help !4 AnswersMathematics9 years ago
Use Newton's method to find all the roots of the equation correct to 6 decimal places.
f(x)= - x^4 +x +1
f ' (x)= - 4x^3 +1
Okay so I found the derivative, and I have the original function.
I want to use the calculator to approximate with different values for initial points until I find the right root ( when the calculator begins putting out the same answer for each initial point).
The problem is, I don't remember how to do this on the calculator.
I have a TI -83. Can someone lead me through the steps to do this on the calculator, please?
I have a test soon so please tell me if I have this right.
To determine intervals of increase/decrease, find f ' (x) and it's critical points; then do the sign chart, plug those random numbers to the right and left of those critical point(s) while plugging them inside f ' (x).
To determine the point at which there is a local maximum or minimum you plug the critical points you got from f ' (x) and plug them back into the original equation f to get the height (the y value ). Now that you have the point you could determine if it was a local max or min by the sign chart you drew for f ' (x) and if it is + on the left of that critical point and - to the right of that c. point it is a maximum; vice versa.
To determine the concavity you find the 2nd derivative f '' (x) and you can use the critical points from f ' OR you can find the critical points for f '' (x) and then you plug the critical points ( whichever option you choose) back into f '' ( x) to determine the concavity. Using the sign chart again.
Correct me if I'm wrong !
When I'm doing the increasing decreasing test, and I pick random numbers far to the side of each critical number, do I use the f(x) function or the f ' (x) to plug those x values into?
F(x)= e^(2x) + e^ (-x)
I know I need to find the derivative to get the critical points that determine the increasing/decreasing intervals.
I also know I need to find the 2nd derivative to get the critical points that determine the concavity ( concave up/concave down.
To get the 1st derivative I used the chain rule on both parts of the f(x) and I got
f ' (x) = 2e ^ (2x) - e ^( - x)
I used the chain rule to get the 2nd derivative too.
f ' ' (x) = 4e^ (2x) + e ^ ( - x)
The problem is I don't know how to solve these functions for x. I know I am supposed to set them equal to zero.
0= 2e ^ (2x) - e ^ ( - x)
And I know that I am supposed to convert the exponential function to the natural log Ln. But I don't know what to do after that. Please help !
Please just show me the process. The answer in the book for the f ' (x) critical point is - 1/3Ln2.
Okay. So I'm beginning to wonder if I'm doing the process wrong. When I have a function, I take it's derivative to find the absolute minimum and maximum on a given interval: let's say [2,4].
I set the derivative equal to zero and solve for x. I get some value (s). Like, 3 or something.
Then I plug 3, 2, and 4 back into the original equation? or the derivative equation?
At first I was getting the answers write. But the answers in the book started getting weird.
So, if there is a y in the equation, but no x, do I have to do implicit differentiation?
Or can I treat y as if it were an x in an f(x) function?
For this example it is called g(y) and has y ' s in a quotient. I was thinking of just doing the quotient rule, and then finding the extrema with respect to y. Is this right?
I am supposed to round to 3 significant figures. It says that if a number can't be expressed, then say so.
So I'm wondering, if a number is 20.0 you can be expressed. But it it's just 20, without a decimal and a zero following after, it can't be expressed technically right?
Y= (2t) / (2 + sqrt(t))
And show me the steps?4 AnswersMathematics9 years ago