Calculus Archive: Questions from May 29, 2023
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find y' of each function by using the differentiation rules
(a) \( y=3 x^{2}-4 x \) (b) \( y=\left(x^{5}+1\right)^{300} \). (c) \( y=\frac{2 x^{3}+x}{1-x} \) (d) \( y=\sqrt{\frac{x}{x+1}} \) (e) \( y=\left(x^{3}+x+1\right)\left(x^{2}+5\right) \) (f) \( y=\left2 answers -
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Evaluar la integral ∫ ∫ s F•N dS para F(x,y,z)=<y,-x,z> y S es el helicoide, cuya representación paramétrica Φ(u,v)= <ucosv, usenv, v>, para 0≤u≤1 y 0≤v≤3π
10. Evaluar \( \iint_{S} \dot{F} \cdot \dot{N} d S \) para \( \dot{F}(x, y, z)=\langle y,-x, z) \) y \( S \) es el helicoide, cuya representación paramétrica \( \phi(u, v)=\langle u \cos v, u \) sen2 answers -
Evaluate the following integrals:
\( \begin{array}{l}\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\left(\sec ^{2}(x)-2 x\right) d x \\ \int_{-\pi}^{\frac{\pi}{2}}\left(\sin \left(\frac{x}{4}\right)+\cos \left(\frac{3 x}{2}\right)\right) d x\en2 answers -
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Evalúa la integral de línea donde C es la curva dada. ∫xyz ds C: x= 2sint, y= t, z= -2cost, 0 ≤ t ≤π2 answers
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Solve the following using laplace transforms
3. \( y^{\prime \prime}-3 y^{\prime}+2 y=12 e^{4 t} \quad ; y(0)=1, y^{\prime}(0)=0 \)2 answers -
2. Find \( \frac{d y}{d x} \) for each of the following: a) \( y=8 \sin (5 x-2) \) b) \( y=-7 \cos x \) c) \( y=5 x^{3} \sin x \) d) \( y=2 \pi \sin ^{3} x \)2 answers -
Resuelve la ecuación diferencial usando el método de coeficientes indeterminados. 1) \( y^{\prime \prime}-16 y=2 e^{4 x} \) S: \( C_{1} e^{4 x}+C_{2} e^{-4 x}+\frac{1}{4} x e^{4 x} \) 2) \( y^{\prim2 answers -
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8. En las matrices aumentadas siguientes \( x \) es un parámetro real. a) \( \left[\begin{array}{rrr|r}3 & 1 & 1 & 1 \\ 0 & -1 & 4 & 4 \\ 0 & 0 & 2-2 x & 2-2 x\end{array}\right] \) b) \( \left[\begin2 answers -
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Sketch the following surfaces: a. \( 4 x^{2}+y^{2}=36 \) b. \( z=x^{2}+4 y^{2} \) c. \( y=x^{2}+z^{2} \)2 answers -
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Find the exact value of each expression. (a) \( \ln e^{-7}= \) (b) \( e^{\ln 3}= \) (c) \( e^{\ln \sqrt{3}}= \) (d) \( \ln \left(1 / e^{3}\right)= \)2 answers -
dx/dy = e^4x+3y
Resuelva la ecuación diferencial dada por separación de variables. \[ \frac{d y}{d x}=e^{4 x+3 y} \]2 answers -
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Given \( \cos (x+y)=\sin x \sin y \), find \( \frac{d y}{d x} \) by implicit differentiation. Select one: a. \( \frac{\sin (x+y)+\cos x \sin y}{\sin (x+y)+\sin x \cos y} \) b. \( -\frac{\cos (x+y)+\co2 answers -
Find \( \iint_{D}(5 x+3 y) d A \) where \( D=\left\{(x, y) \mid x^{2}+y^{2} \leq 4, x \geq 0\right\} \)2 answers -
Find \( \iint_{D}(5 x+3 y) d A \) where \( D=\left\{(x, y) \mid x^{2}+y^{2} \leq 4, x \geq 0\right\} \)2 answers -
Evaluate \( \iiint_{E} 3 x z d V \) where \( E=\{(x, y, z) \mid 0 \leq x \leq 2, x \leq y \leq 2 x, 02 answers -
Evaluate \( \iiint_{E} 2 x z d V \) where \( E=\{(x, y, z) \mid 2 \leq x \leq 3, x \leq y \leq 2 x, 02 answers -
Evaluate \( \iiint_{E} 2 x z d V \) where \( E=\{(x, y, z) \mid 2 \leq x \leq 5, x \leq y \leq 2 x, 02 answers