Suppose we have the paraboloid $z=x^2+y^2$ and the plane $z=y$. Their intersection produces a curve $C$, and certain surfaces bounded by it, for example the disc $S$ which directly fills the area of $C$ and the paraboloid $S’$ given by $z=x^2+y^2$ which extends from $C$ downwards and is bounded by $C$. My question is on […]

Find the parametric form $S(u, v)$ where $a \le u \le b$ and $c \le v \le d$ for the triangle with vertices $(1, 1, 1), (4, 2, 1),$ and $(1, 2, 2)$. I am told that one parameterisation is $S(u, v) = (1 + 3u, 1 + u + v, 1 + v)$ for […]

How can I prove the following? $\gamma (t)$ is unit speed, $\dot \gamma(t) \not= 0 \Rightarrow \ddot \gamma(t)$ is perpendicular to $\gamma(t)$ I don’t really see where a problem would arise when $\dot \gamma(t)=0$ would cause such a problem

Intereting Posts

Integral $\int_{0}^{A}\frac{\exp(-2\pi iwx)}{x-i}dx $
Natural cubic splines vs. Piecewise Hermite Splines
Proof that two spaces that are homotopic have the same de Rham cohomology
Show that the sum $\frac {1}{p_1} + \frac {1}{p_2} +\frac {1}{p_3} +…+\frac {1}{p_n}$ is never an integer,where $p_i$'s are primes,$ 1\le i \le n$.
Maximising sum of sine/cosine functions
solve for m by rewriting the equation (transposition)
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
Convergence in the product topology iff mappings converge
Riemann Hypothesis, is this statement equivalent to Mertens function statement?
Can all math results be formalized and checked by a computer?
Complex substitution allowed but changes result
Are there concepts in nonstandard analysis that are useful for an introductory calculus student to know?
Proof convergence of random variables (almost sure)
Prove that for any $1 < p < ∞$ there exists a function $f ∈ L_p(μ)$ such that $f \notin L_q(μ)$ for any $q > p.$
Mapping natural numbers into prime-exponents space