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Mathematics
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Roma_Rayado
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question
14
Prove that $\,\int_0^1 \sqrt{1+x^2}\,\mathrm dx\le \int_0^1 \sqrt{1+x}\,\mathrm dx\,,\,$ proof verification.
Aug 21, 2023
question
4
If $a_1=1$ and $a_{n+1}=3-\frac{1}{a_n}$, show that the sequence converges and find the limit.
Nov 17, 2023
question
2
Using de Moivre's Theorem, show that: $\cos(5\theta)=\cos^5\theta-10 \cos^3\theta \sin^2\theta+5 \cos\theta \sin^4\theta$
May 14, 2023
question
2
Find the indeterminate values of $x_1$ and $y_1$ if $\vec x=(x_1,-2,1,-1)$ and $\vec y=(-2,y_2,-1,-2)$ and $\lVert \vec x\rVert=2\lVert \vec y\lVert$
Feb 12
question
2
Given $d(\vec{x},A):=\text{inf}\{\lVert\vec{x}-\vec{y}\rVert:\vec{y}\in A\}$, show that $f^{-1}(\{0\})=\overline{A}$
Apr 19
question
1
Having $z,w,a,b\in \mathit C$ Show that the segment $zw$ is parallel to $ab$ iff: $\frac{z-w}{\bar z-\bar w}=\frac{a-b}{\bar a-\bar b}$
May 15, 2023
question
1
Let $f:R\to R$ be a continuous function, and let $F:R\to R$ given by: $F(x)=\int_a^x xf(t)dt$, justify if it's differentiable
Sep 18, 2023
question
1
Find a explicit formula for $f(x)$ where $\phi(t)=\int_0^x f(t)dt=\int_x^1 t^2f(t)dt+\frac{x^{16}}{8}+\frac{x^{18}}{9}+C$
Nov 30, 2023
question
1
Proving divergence or convergence of $\sum_{i=0}^\infty \frac{-n}{2n+5}$ [closed]
Dec 28, 2023
question
1
Show that $\frac{1}{\sqrt{n}}\lVert x\rVert_1\le\lVert x\rVert_2\le \lVert x\rVert_1$
Feb 13