Evaluate this indefinite integreal
S = integral
S 1/(9+x^2)^2
This has been driving me and my friend nuts.
We tried partial fractions only to realise that it brings us back to the same thing because its not a polynomial over a polynomial, we tried by parts and it did not help and we...
(purpose is to find molar mass)
At the start we dissolved 0.945 grams of unknown weak acid into water and made it up to
100 ml
Then we used 25 ml of that solution and titrated it until the end point.
Now , this is a monoprotic acid so it's going to take 1 mol of acid to neutralise 1 mol of...
Homework Statement
A 150 grams particle oscillating in SHM travels 24 cm between the two extreme points in its motion with an average speed of 60cm/s
Find
a) angular frequency
b) the maximum force on the particle
C) the maximum speed
The Attempt at a Solution
My first...
Homework Statement
A 2.5 kg block is on a 53 degres incline for wich Uk = 0.25 and Us = 0.5 . Find its acceleration given that (a) it is initially at rest.
I don't know how to approach this. We have kinetic friction when an object slides. This object starts at rest. Does that mean...
lim as x goes closer to minus infinity.
x^4 + x^5
now visibly the answer is minus infinity since the equation are simple. But aside from saying x^5 is bigger then x^4 could there be anything else to do ?
Homework Statement
I need to find a tangent line equation but my main problem is isolating actually.
sqrt ( 2x + 2y ) + sqrt ( 3xy) = 13
The Attempt at a Solution
0.5 ( 2x + 2y ) ^ -0.5 (2+2y') + 0.5(3xy) ^ -0.5 ( 3 ( y + y' x ) ) = 0
this is where I get stuck
Homework Statement
Let
arctan (\sqrt{3x^2 -1})
then dy/dx
Well I know that the derivative of arctanx is
1/ 1 + x ² but when I got something other then simply x I don't know how to proceed
Homework Statement
If f(x) = (3 x )(sin x) (cos x), find f'( x ).
A question I have is , is there anything special to do when you have 3 products instead of 2
The Attempt at a Solution
Well I used the product rule as if am multipling
(3xsinx) (cosx)
but that doesn't...
Homework Statement
If d/dx (f(2x^4)) = 8x^5
Calculate f'(x)
Homework Equations
The Attempt at a Solution
Well , we have been only doing derivatives for 2-3 class and its new for me.
From what I understand in this question is.
You have a function f(x) = something
The...
Homework Statement
| b + 2 |
----------
b + 2
Lim b ---> - 2 - ( from the left )
The Attempt at a Solution
Am I right if I say the absolute value can be simplified into
-b - 2 because the way we are appraching 2 would give me a negative number so I would have to make it...
Homework Statement
1/b - 1/3
-----------
b-3
Lim b ----> 3
Homework Equations
The Attempt at a Solution
This is driving me nuts. I always end with 0 but thats not the answer.
I tried direct substitution and it didn't work.
I tried plugging in 2.999999999 but it...
Homework Statement
Find in terms of the constant a
Lim h --- > 0
8 (a+h)² - 8a²
-----------------
h
The Attempt at a Solution
I have no idea how to even approach it so some pointers would be nice.
It hasn't been long since I started calculus. I am not sure...
Homework Statement
A lead ball is dropped into a lake from a diving board 5.0 m above the water. After entering into the water it sinks into the bottom with a constant velocity which it hit the water for 3 seconds. and hits the bottom of the lake. How deep is the late ?
Homework Equations...
Homework Statement
An object is thrown up from the top of a building 50 m high. It rises to a maximum high of 20 m above the roof.
A) when does it land on the ground
B) At what velocity does it land ?
C) When is it 20 m below the roof?
Homework Equations
The 4 kinematics equations...