Recent content by wshfulthinker

yeah it says cosh(arcsinh(x)) = √(1 + x²) But i want to know how you get that from cosh(arcsinh(x)). I have been trying to find proof for it.edit: never mind, i have figured it out now! let y = arcsinhx x = sinh(y) use the identity cosh^2(y) - sinh^2(y) = 1 etc

Sorry, i was trying to cut out the part i needed help with, this is the whole question: Evaluate the following indefinite integral: ∫1/(x² + 4)^(3/2).dx Here is my working out; put x = 2sinh(θ) dx/dθ = 2cosh(θ) dx = 2cosh(θ).dθ (x² + 4)^(3/2) = (4sinh²(θ) + 4)^(3/2) Since...

Homework Statement I need to solve: 1/4tanh(θ) + c Homework Equations x=2sinh(θ) θ = arcsinh(x/2) The Attempt at a Solution I worked out that since tanh(θ) = sin(θ)/cosh(θ) then 1/4tanh(θ) + c = x/8cosh(θ) + c But i don't know how to work out cosh(θ) or cosh(arcsinh(x/2))...

Okay okay... so i am pretty crap with vectors! But i got the answer finally! :D I found a book which wrote the direction in the i + j form which made more sense to me and didn't make me think it was a point. And yes, i got the answer so i think i kind of understand it now... Thankyou! :)

Hi, thanks for the welcome and showing me the symbols! I don't really get it though! where do i use the point (1,2). I'm not even sure what i worked out, i followed the method that were in my lecture notes which were worded almost the exact same way as my actual question (except it said find...

Homework Statement Consider the function: z=f(x,y)= log(x^2 + y^2) (x,y)=/=(0,0) Calculate the directional derivative of f(x,y) at (x,y)=(1,1) in the direction of the vector (1,2) The attempt at a solution When i tried to work out the unit vector from the point (1,1) to...

Hi, thankyou so much for your reply. I tried it and it worked! i shall write it down and remember that forever now! Also, sorry about posting in the wrong section! I can't believe i did that because i took so long to check that my post was right.. i guess i forgot to check if i had clicked on...

Homework Statement Consider the differential equation: y''+10y'+25y= f(x) Find a particular solution if f(x) = 32xe^(-x) Homework Equations I already did the general solution when f(x)=0 and that is Ae^(-5x) + Bxe^(-5x) The Attempt at a Solution I tried yp=axe^(-x) and got a=...