Calculus Archive: Questions from September 11, 2022
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Evaluate the integral. \[ \int \cos ^{4} \theta \sin 2 \theta d \theta \] \[ \frac{2}{5} \cos ^{4} \theta+C \] \[ -\frac{2}{7} \cos ^{7} \theta+C \] \[ -\frac{1}{3} \cos ^{6} \theta+C \] \[ \frac{1}{61 answer -
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67. Multiple Choice Let \( f(x)=\int_{a}^{x} \ln (2+\sin t) d t \). If \( f(3)=4 \), then \( f(5)= \) (A) \( 0.040 \) (B) \( 0.272 \) (C) \( 0.961 \) (D) \( 4.555 \) (E) \( 6.667 \)1 answer -
1.find the total differential 2.considere the function a)evaluate b)calculate c)use the the total differential of dz to approximate z
I. Halle el diferencial total a) \( z=e^{x} \operatorname{sen}(y) \) b) \( w=\frac{x+y}{z-3 y} \) II. Considere la función \( f(x, y)=y e^{x} y \) trabaje: a) Evaluar \( f(2,1) \) y \( f(2.1,1.05) \)1 answer -
Simplify the following expression. a. \( \frac{\tan A-\tan (A-B)}{1+\tan A \tan (A-B)} \) b. \( \quad \cos (y) \cos (-2 y)-\sin (y) \sin (-2 y) \)2 answers -
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Evaluate the integral \( \int x^{2} \cos (3 x) d x \) Select one: a. \( \frac{1}{3} x^{2} \sin (3 x)+\frac{2}{27} \sin (3 x)-\frac{2}{9} x \cos (3 x)+C \) b. \( \frac{1}{3} x^{2} \sin (3 x)-\frac{2}{21 answer -
Carlos decides to ride a regular sale of rectangular shape (see figure) a semicircle in The top. What should be the dimensions for the window that maximizes the area with a perimeter 16 ft. total.
Resuelva: Carlos decide montarle a una ventada regular de forma rectangular (ver figura) un semicírculo en el tope. Cuáles deben ser las dimensiones para la ventana que máximicen el área con un pe1 answer -
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9) Given \( y=4 \cos (\theta)+10 \sin (\theta) \), find \( \left.\frac{d^{2} y}{d \theta^{2}}\right|_{\theta=\pi}=? \)1 answer -
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\( \lim _{n \rightarrow \infty} \frac{(-1)^{n} e^{\cos \left(4 n^{3 / 2}-18 \sqrt{\sqrt{147 n^{3}-1}}\right)}+\sqrt{2 n^{2}+2 n+3}}{2 n+3} \)1 answer -
Rotate the ellipse x^2/a^2 + y^2/b^2 = 1 around the x axis to generate the volume of an american football as shown in the figure. Calculate the volume using (a) the slicing method and (b) the washer m
2. Rota la elipse \( x^{2} / a^{2}+y^{2} / b^{2}=1 \) alrededor del eje \( x \) para generar el volumen de una I pelota de "football" americano, como se muestra en la figura. Calcula el volumen genera2 answers -
Solve the following boundary-walue problem: \( y^{\prime \prime}+9 y=0, ; y(0)=-1, y\left(\frac{\pi}{6}\right)=1 \) \[ y=\cos 3 x+\sin 3 x \] \[ y=-\cos 3 x+\sin 3 x \] \[ y=\cos 3 x-\sin 3 x \] (1) \1 answer -
La solucion por sustitucion de la ecuacion diferencial dada en la foto es:
La solución de la ecuación diferencial \( x d y=\left(y+\sqrt[2]{y^{2}-x^{2}}\right) d x \), es: a. \( 2 c y=c^{2} x^{2}+y \) b. \( 2 c y=c^{2} x^{2}+1 \) C. \( 2 c y=c^{2} x^{2}+x \) d. \( 2 c y=c^1 answer -
Find the derivative of each function. Simplify wherever possible. a. \( f(x)=\left(3 x^{2}+7\right)\left(x^{2}-2 x+3\right) \) b. \( y=\frac{x^{2}-x+2}{\sqrt{x}} \) c. \( y=\frac{x^{2}-2}{2 x+1} \) d.1 answer -
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III. Determine the directional derivative of the function in the dirrction of PQ. IV. Determine the gradient of the function and the direction of maximum growth of the function at the given point.
III. Determine la derivada direccional de la función en dirección de PQ \( f(x, y)=x^{2}+3 y^{2} \) donde \( P(1,1) \) y \( Q(4,5) \). NV. Determine el gradiente de la función y la dirección de m1 answer -
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Find the general solution of \[ y^{\prime}=\frac{4 x\left(y^{2}-9\right)}{x^{2}+5} \] a) \( y=\frac{1-C\left(x^{2}+5\right)^{12}}{1+C\left(x^{2}+5\right)^{12}} \) b) \( y=\frac{3+3 C\left(x^{2}+5\righ1 answer -
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Use the graph of the function \( y=f(x) \) to find the given values, if possible. Estimate when necessary. \[ \lim _{x \rightarrow 0^{-}} g(x)= \]1 answer -
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