Calculus Archive: Questions from January 27, 2023
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Match each expression with an equivalent one. In this question \( x, y>1 \) \[ \begin{array}{lll} y=3^{x} & e^{y}=\frac{e^{x}}{e^{3}} & x^{y}=3 \\ e^{x-y}=3 & y=e^{x} & y=x \end{array} \] 1. \( y=x-32 answers -
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Find the Area aswell.
\( y=\sqrt{x-1}, y=0, x=5 ; \quad \) about the \( x \)-axis Sketch the region enclosed by the given curves. Decide whether to integrate with respect to \( x \) or \( y \). Draw a typical approximatin2 answers -
Problema .. : Se desea construir un pequeño centro comercial cuyo plano está dibujado más adelante. El centro comercial debe consistir de ocho tiendas rectangulares iguales( identificadas con una \3 answers -
ll. calculate the volume of the given figure lll. rewrite the integral using the order dxdzdy. then comment on whether or not it is convenient to change the coordinates to cylindrical or spherical and
II. Calcule el volumen del sólido en la figura dada. III. Reescriba el integral utilizando el orden dxdzdy. Luego comente si es o no es conveniente hacer cambio de coordenadas a cilíndricas o esfér0 answers -
(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=\sin \left(\frac{5 x}{y}\right) \) \( f_{x x}(x, y) \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \) \( f_{y y}(x, y)= \)2 answers -
Evaluate: \( \int \frac{\sin (\sqrt[11]{x})}{x^{\frac{10}{11}}} d x \) Answer: \[ \int \frac{\sin (\sqrt[11]{x})}{x^{\frac{10}{11}}} d x= \]2 answers -
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(d) \( \sin \left(\tan ^{-1} x\right)= \) (e) \( \cos \left(\sin ^{-1}\left(\frac{x}{2}\right)\right)= \)2 answers -
\( y^{\prime}\left(\frac{\pi}{4}\right) \) if \( y(x)=(8 \cos x)^{x} \) \( y^{\prime}\left(\frac{\pi}{4}\right)= \)2 answers -
QUESTION 1: QUESTION 2:
Evaluate \( \iiint_{E}(x+y-4 z) d V \) where \( E=\left\{(x, y, z) \mid-3 \leq y \leq 0,0 \leq x \leq y, 02 answers -
Completa los componentes para calcular con \( n \) particiones la Integral Definida: \[ \begin{array}{l} \int_{3}^{0} 24 x^{2} \text { más }-4 x+3 d x \\ \triangle x=1 / n \\ x_{i}= \\ f\left(x_{i}\r2 answers -
\( \int_{-4}^{4}\left[5 x \sin ^{16}(-8 x)+9 x^{9}\right] d x= \) \( \int_{-8}^{8}\left[\exp \left(-8 t^{4}\right) \sin \left(-3 t^{15}\right)+\cos (-8 t)+\frac{\sin (8 t)}{1+t^{18}}\right] d t= \)2 answers -
\( \frac{d y}{d x} \) \( y=-2 x^{3}+\frac{4}{5 \sqrt[5]{x^{4}}}-\frac{3}{x^{2}} \) \( y=\cos ^{2} \sqrt{\sin (\tan \pi x)} \) \( y=\frac{-2 x^{2}-5}{\cos 2 x^{3}} \)2 answers -
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