Advanced Math Archive: Questions from January 24, 2023
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2. Sea la superficie parametrica: r(u,v)=ui+2cosvj+2senvk con 0 ≤ u ≤ 1 y 0 ≤ v ≤ π. (a) Calcule el area de la superficie mediante la integral de superficie. (b) Determine la masa que tendria
2. Sea la superficie paramétrica: \[ \vec{r}(u, v)=u \hat{\imath}+2 \cos v \hat{\jmath}+2 \operatorname{sen} v \hat{\mathrm{k}}, \] con \( 0 \leq u \leq 1 \) y \( 0 \leq v \leq \pi \) (a) (1 punto) C2 answers -
3. Determine el flujo del campo: F(x,y,z) = z^2i+3xj-zk, a traves de la superficie parametrica r(u,v) = ui + cos vj + sen^2 vk, con 0 ≤ u ≤ 1 y 0 ≤ v ≤ π.
3. (1 punto) Determine el flujo del campo: \[ \vec{F}(x, y, z)=z^{2} \hat{\imath}+3 x \hat{\mathbf{j}}-z \hat{\mathrm{k}}, \] a través de la superficie paramétrica \( \vec{r}(u, v)=u \hat{\imath}+\c2 answers -
URGENT PLEASE
\( \sin \left(\frac{\pi}{4}+x\right)+\sin \left(\frac{\pi}{4}-x\right)=\sqrt{2} \cos x \)2 answers -
Use Green's theorem to set up a line integral that allows us to calculate the area of the region bounded by the curve . The line integral must be developed in such a way that there remains a usual int
(5 pts.) Utilice el teorema de Green para plantear una integral de linea que permita calcular el área de la región limitada por la curva \( x^{2}+y^{2} / 4=1 \). La integral de linea debe desarrolla2 answers -
Solve the following differential equations (a) \( y^{\prime}=x^{3}+5 \) (b) \( y^{\prime \prime}=2, \quad y(0)=1, y^{\prime}(0)=2 \) (c) DE: \( y^{\prime \prime \prime}=x \) IC: \( y(0)=0 \quad y^{\pr2 answers -
Perform the following integrations: 1) \( y^{\prime}=6 e^{6 x} \sin \left(e^{6 x}\right) \Rightarrow y= \) 2) \( y^{\prime}=\frac{x+3}{x^{2}+6 x+12} \Rightarrow y= \) 3) \( y^{\prime}=\cos (6 x) \sqrt2 answers -
Solve the initial-value problem \( x y^{\prime}=y+x^{2} \sin x, y\left(\frac{\pi}{3}\right)=0 \). Answer: \( y(x)= \)2 answers -
Solve the initial-value problem \( x y^{\prime}=y+x^{2} \sin x, y\left(\frac{\pi}{3}\right)=0 \). Answer: \( y(x)= \)2 answers -
2 answers
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4. Simplify \( \frac{2 \tan \frac{\pi}{8}}{1-\tan ^{2} \frac{\pi}{8}} \cdot-7=2+a r \alpha \) a \( \frac{1}{\sqrt{3}} \) b. \( \sqrt{3} \) c. \( \frac{1}{\sqrt{2}} \) d. 12 answers -
Factor the expression \( \sin ^{2} \theta-\sin \theta-12 \). a. \( (\sin \theta-3)(\sin \theta+4) \) c. \( (\sin \theta+3)(\sin \theta-4) \) b. \( (\sin \theta-1)(\sin \theta+12) \) d. \( (\sin \theta2 answers -
5. Prove that the following wffs are valid arguments. (a) \( [8] \) \[ (\exists x)(M(x) \wedge(\forall y) R(x, y)) \wedge(\forall x)(\forall y)(R(x, y) \rightarrow T(x, y)) \rightarrow(\exists x)(M(x)1 answer -
Let \( x, y, z \) be (non-zero) vectors and suppose \( w=2 z \). If \( z=2 y-4 x \), then \( w=|\quad| x+\quad y \). Using the calculation above, mark the statements below that must be true. A. \( \op2 answers