True of False inequality graphing questions(plug in ) February 14

Point (6,y) is a solution of the inequality 12y+x>0 for any value of y.I got false since y could be negative infinite and that plus 6 would be less than 0. Is that correct>Also, in - Point (a,−a) is a solution of the inequality 6x+y>0 for any val

How is the second derivitive derived February 14    2

As everyone knows that the derivitive of a function is $\frac{dy}{dx}$The question is: Why is the second derivitive: $$\frac{d^2y}{dx^2}$$If anyone is able to tell me how this second derivitive notation is derived, please do.This is just notation. Le

Find all entire $f$ such that $f(f(z))=z$. February 14    3

Suppose $f:\mathbb{C}\to \mathbb{C}$ is entire. If $f(f(z))=z$, find all such $f$.Can we find $f$ such that $f(f(z))=z^2$?How about $f(f(z))=e^z$? Ideas: For #1, we can show that $f$ must be a bijection, since $f$ failing to be either injective or su

find all value of z belong to C February 14

find all value of z belong to C
find all value of z belong to C such that $$ e^z = -3i$$my try $$e^z=e^{x+iy}$$.$$-3i = r*e^(i*0)$$ take ln both sides $$z =ln(-3i)$$stuck here , need help to solve it please

How many ways are there to arrange these letters February 14

So I've been working out how many ways there are to arrange the letters of probabilistic. I came up with 518918400 ways. The next thing I want to figure out is out of those ways, how many of them have all the b's always come before the i's. In other

Find the original function by using convolution theorem February 14

Find the original function by using convolution theorem
Seems like I don't know how to apply convolution theorem on this problem properly, I would appreciate some help and a brief explanation how did you solve it if you do it. \begin{equation}\fr ...

Integral of $\frac{x}{\sqrt{1+x^5}}$ February 14    3

I am trying to calculate the following integral: $\displaystyle\int_0^\infty \frac{x}{\sqrt{1+x^5}}\, dx$But I can't seem to find a primitive for that function. I was trying to find a good substitution, but was unable to. Also, attempting to use part

Integrating $\frac{1}{(ax^2+bx+c)^n}$ two ways February 14    1

Could someone please show me how to do the indefinite integral of$$\frac{1}{(ax^2+bx+c)^n}$$a) using real analysis (hard)b) using complex analysis (nice factoring)and show they give the same answer, without using any simplifiers into $1 + t^2$ or oth

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