0
votes
2answers
40 views

Is this a typo, or am I missing something?

I have a handout for my precalc II class. It says $\sinh(-x) = -\sin(x)$ It should be $\sinh(-x) = -\sinh(x)$ right? I don't see how a negative input could make a hyperbolic function circular.
0
votes
1answer
34 views

Find a linear combination of $u_n$'s satisfying $u(x,1) = \sin(2\pi x) -\sin(3\pi x)$

I have the following problem: $$u_n(x,y) = \sin(n\pi x)\sinh(n\pi y), \;\;\;n = 1, 2, 3, ...$$ Find a linear combination of the $u_n$'s that satisfies: $$u(x,1) = \sin(2\pi x) -\sin(3\pi x)$$ Any ...
3
votes
4answers
258 views

If $f$ is holomorphic and $\,f'' = f$, then $f(z) = A \cosh z + B \sinh z$

Suppose $f$ is holomorphic in a disk centered at the origin and $f$ satisfies the differential equation $$f'' = f.$$ Show that $f$ is of the form $$f(z)=A \sinh z + B \cosh z,$$ for suitable constants ...
1
vote
3answers
49 views

Showing that $\sinh(\mathrm{e}^z)$ is entire

I am attempting to show that $\sinh(\mathrm{e}^z)$, where $z$ is a complex number, is entire. The instructions of the problem tell me to write the real component of this function as a function of $x$ ...
0
votes
1answer
44 views

Rewriting a hyperbolic equation in standard form

$9x^2-4y^2-72x$ = 0 How would that be done? So far, I got up to $\frac{9(x^2-8x)}1-\frac{4(y-0)^2}1=0$
1
vote
2answers
551 views

Hyperbolic Functions

Hey everyone, I need help with questions on hyperbolic functions. I was able to do part (a). I proved for $\sinh(3y)$ by doing this: \begin{align*} \sinh(3y) &= \sinh(2y +y)\\ &= ...
0
votes
1answer
123 views

Integration by parts

Question 2)b) part (ii) is the section that I'm having trouble with: I don't understand the method used in the solutions; how would you deduce the first line or is that something you should know? ...
1
vote
1answer
377 views

Inverse Laplace Transform involving $\cosh$.

While doing an assignment on solving a PDE I stumbled into the following inverse Laplace transform question (involving $\cosh$? I can't believe it). Mathematica gives no solution and I have no idea ...