If the tangent at $(x_0,y_0)$ to the curve $x^3+y^3=a^3$ meets the curve again at $(x_1,x_1)$ then prove that $\frac{x_0}{x_1}+\frac{y_0}{y_1}=1$
112857
Tangent to curve $x^3+y^3=a^3$ meets it again.
55197
Roots of $ x^3-3x+1$
107824
Proof by induction that $a_0 = 1, a_1 = 1, a_n=2a_{n-1} + 3a_{n-2}$ satisfies $a_n = \frac12 (3^n) + \frac12 (-1)^n$
15287
Proving that second derivative is perpendicular to curve
96388
Prove $\sin(x)\tan(x) > x^2$ for $x \in ( \,0, \frac{\pi}{2}) \,$
109288
Prove that $x^3+y^3+z^3-3xyz=1$ defines a surface of revolution
103416
Proving area under curve
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
144713
Simple Calculus Proof
12375
Prove $\lim_{(x,y) \to (0,0)} \frac{x^3y}{x^4+y^2} = 0$
37357
Rectifiability of a curve
85944
Prove $ \sin x + \frac{ \sin3x }{3} + ... + \frac{ \sin((2n-1)x) }{2n-1} >0 $
25981
Prove that $\sum_{k=0}^n a_k x^k = 0$ has at least $1$ real root if $\sum_{k=0}^n \frac{a_k}{k+1} = 0$
89567
Common tangent to a curve
145019
Prove that $\sum_{n=0}^\infty \frac{(-1)^n}{3n+1} = \frac{\pi}{3\sqrt{3}}+\frac{\log 2}{3}$
19828
Show that $\frac{x^3}{x^2+y^2}$ is not differentiable at $(0,0)$, even though all directional derivatives exist
123976
Slope of the tangent line, Calculus