Can someone help me with a approach? Not looking for a solution just for a hint

Find the equation of the diameter of $3x^2+4y^2=5$ conjugate to the diameter $y+3x=0$. Two problems: The given equation is that of an ellipse $\dfrac{x^2}...

The first derivative can tell me about the intervals of increase/decrease for $f(x)$. The second derivative can tell me about the concavity of $f(x)$. So ...

What does it mean that a set $S$ tautologically implies wff $ \tau$ ? in Enderton introduction to mathematical logic , in page 23 , it define that a set $...

I have been trying to apply De morgan's law in Logic gates, and realized I am not quite sure if I can use it on my own if given a random problem, whi...

Obtain the general solution of the different equation $$\frac{d^2y}{dx^2}-3\frac{dy}{dx}+2y=20\sin x.$$ Hence find the particular solution for which : $y=...

All of the theorems I have found in my textbook and on the internet just state the converse; is it true both ways?

Calculate $\int{ \frac{e^z}{z^2(z^2+3)}}dz$ over the rectangle $x=2,x=-2 ,y=2,y=-2$. What i did is find the roots of $z^2+3$ break the $\frac{1}{z^2+3}$ i...

Evaluate $$\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}$$ My attempt, I changed it into $$\sum_{n=1}^{99} \frac{n}{(n+1)!}$$ I really don�...

How many numbers from $1$ to $99999$ have a digit-sum of $8$? Why is the answer ${8+4\choose 4}$? Does the following method work? Answer is the number of ...