Calculus Archive: Questions from October 19, 2022
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ferentiate the function: \( y=\cos ^{2}(\sin 4 x) \) \[ \begin{array}{l} y^{\prime}=-2 \cos (\sin 4 x) \sin (\sin 4 x) \\ y^{\prime}=2 \cos (\sin 4 x)(4 \cos 4 x) \\ y^{\prime}=-4 \cos (4 x) \sin 2(\s2 answers -
2 answers
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PLEASE SOLVE ASAP
Question 4 Let \[ f(x, y, z):=\frac{\cos \left(121 x^{2}+121 y^{2}\right)-e^{209 x^{2}+209 y^{2}}+39 x^{6} y^{4}}{11 x^{2}+11 y^{2}}+z \cos (x) \] Find \[ \lim _{(x, y, z) \rightarrow(0,0,20)} f(x, y,2 answers -
PLEASE SOLVE ASAP
Question 4 Let \[ f(x, y, z):=\frac{\cos \left(121 x^{2}+121 y^{2}\right)-e^{209 x^{2}+209 y^{2}}+39 x^{6} y^{4}}{11 x^{2}+11 y^{2}}+z \cos (x) . \] Find \[ \lim _{(x, y, z) \rightarrow(0,0,20)} f(x,2 answers -
given vectors: A=j+2k y B=i + 2j +3k. c=3i-2j-k
Problemal. Dados los vectores: \( \quad \mathbf{A}=\mathbf{j}+2 \mathbf{k} \) y \( \mathbf{B}=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k} \quad \mathrm{C}=3 \mathrm{i}-2 \mathrm{j}-\mathrm{k} \) Calcular: A.2 answers -
calculate the angle od the two vectors.
Problema2. Dados los vectores: \( \mathbf{A}=\mathbf{j}+2 \mathbf{k} \) y \( \mathbf{B}=\mathbf{i}+2 \mathbf{j}+3 \mathbf{k} \). Calcular el ángulo entre los dos vectores:2 answers -
indicate which pair of vectors are perpendicular?
Dados los vectores: \( : \mathbf{A}=-\mathbf{i}+\mathbf{j}, \mathbf{B}=-\mathbf{i}-\mathbf{j}-2 \mathbf{k}, \mathbf{C}=2 \mathbf{j}+2 \mathbf{k} \) Indique cuál (ó cuales) parejas de vectores son pe2 answers -
calculate the area and the height of a parallelogram which base is given by the vector B= i + 2j + 5k and one of the sides of the vector c= i + 3j - k
Problema4. Calcular el área y la altura de un paralelogramo cuya base está dada por el vector \( B=i+2 j+5 k \) y uno de sus lados por el vector \( C=i+3 j-k \)2 answers -
Consider the electric field ... Calculate the electric flux through the surface parameterized by... where... Note: The electric flux is given by the surface integral
Considere el campo eléctrico \( E=y \hat{i}-x \hat{j}+z \hat{k} \). Calcule el flujo eléctrico que atraviesa a la superficie parametrizada por \( r(u, \nu)=u \cos (\nu) \hat{i}+u s e n(\nu) \hat{j}+2 answers -
Compute the exact derivative. \[ f(x)=\cot ^{-1}(x) \] \[ f^{\prime}(0.6)= \] If \( f(x)=2 \) \( \frac{12}{36 x^{2}+1} \)2 answers -
2 answers
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number 7 please
Find all equilibrium points of the autonomous system. 1. \( x^{\prime}=-x+x y \) 2. \( x^{\prime}=y(x+3) \) \( y^{\prime}=y-x y \) \( y^{\prime}=(x-1)(y-2) \) 3. \( x^{\prime}=(x-2)(y+1) \) 4. \( x^{\2 answers -
(-16)^1/4 find 4 square root please detail solve
\( -16=16(\cos \pi+i \sin \pi) \) \( \sqrt[4]{-16}=\left(\sqrt[4]{16}\left(\cos \frac{\pi+2 k \pi}{4}+i \sin \frac{\pi+2 k \pi}{4}\right)(k=0,1,2,3)\right. \) \( w_{1}=2\left(\cos \frac{\pi}{4}+i \sin2 answers -
A cyclist climbs a mountain along the path shown. It makes a full turn around the mountain to reach the top, while its angle of climb is constant. During the trip it exerts a force described by the ve
Un ciclista sube una montaña a lo largo de la trayectoria que se muestra. Realiza un giro completo alrededor de la montaña para alcanzar la cima, mientras que su ángulo de subida es constante. Dura0 answers -
2 answers
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Find \( \frac{d y}{d x} \) in each of the following: 1) \( y=2 x^{3}-5 x^{2}+8 x-14 \) 2) \( y=\sqrt{\ln x} \) 3) \( y=\ln (\tan x) \) 4) \( y=\sin ^{2}(\ln x) \) 5) \( y=\tan ^{-1}\left(x^{3}\right)2 answers -
\( y=-13 e^{x}+\frac{20}{\sqrt[9]{x}} \) (1 point) Differentiate the function \[ y=-13 e^{x}+\frac{20}{\sqrt[9]{x}} \]2 answers -
59. Determine whether \( f(0) \) exists \[ f(x)=\left\{\begin{array}{ll} x \sin \frac{1}{x}, & \text { if } x \neq 0 \\ 0, & \text {, if } x=0 \end{array}\right. \] 60. \( f(x)=\left\{\begin{array}{ll2 answers -
ind the center, foci, and asymptotes of the hyperbola. 5) \( \frac{(x+2)^{2}}{225}-\frac{(y+5)^{2}}{400}=1 \) A) C: \( (-2,-5) ; F:(-5,-22),(-5,18) ; A: y=\frac{16}{9} x+\frac{7}{45}, y=-\frac{16}{9}2 answers -
SCALCET6 15.3.011. Evaluate the double integral. \[ \iint_{D} 4 y^{2} e^{x y} d A, D=\{(x, y) \mid 0 \leq y \leq 6,0 \leq x \leq y\} \]2 answers -
Match the function with its graph. \[ f(x, y)=(x-y)^{2} \] A \[ f(x, y)=|x|+|y| \] B \[ f(x, y)=\frac{1}{1+x^{2}+y^{2}} \] C \[ f(x, y)=\left(x^{2}-y^{2}\right)^{2} \] [ \[ f(x, y)=\sin (|x|+|y|) \] E2 answers -
find dy/dx in each of the following:
6) \( y=\sec ^{-1}\left(x^{5}\right) \) 7) \( y=e^{3 x} \sec ^{-1} x \) 8) \( y=\frac{1-x^{3}}{x^{2}} \) 9) \( y=\sec ^{-1}(2 x+1) \) 10) If \( y=2 t^{3}-4 t \quad, x=2 t^{2}-7 \)1 answer -
2. Differentiate the following. (a) \( e^{x} \cos x ; \) (b) \( e^{x} \sin x ; \) (c) \( \sec x=\frac{1}{\cos x} \); (d) \( \csc x=\frac{1}{\sin x} ; \) (e) \( \sec x \csc x=\frac{1}{\sin x \cos x} \)2 answers -
2 answers
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help please
Maximize \( p=2 x+y \) subject to \[ \begin{array}{l} x+2 y \leq 11 \\ -x+y \leq 5 \\ x+y \leq 5 \\ x \geq 0, y \geq 0 \end{array} \]2 answers -
2 answers
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1. Find the solutions of the following IVPs or DE. a. \( y^{\prime \prime}-4 y^{\prime}+4 y=e^{2 x} \), \( y(0)=1, y^{\prime}(0)=0 \) b. \( y^{\prime \prime}-2 y^{\prime}=e^{2 x}+3, \quad y(0)=1, y^{\2 answers -
2 answers
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Let \( D=[0,1] \times[0,1]=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} \). Evaluate \( \iint_{D} 2 x^{3} e^{y x^{2}} d A \).2 answers -
Evaluate the two following integrals.
\( \int_{0}^{2} \int_{0}^{y} y^{2} e^{x y} d x d y \) \( \int_{0}^{2} \int_{2}^{x} y^{2} e^{x y} d y d x \)2 answers -
Determine mass and center of mass of the solid with given density bounded by the graphs of the equations. Clearly state and evaluate the triple integral that allows you to determine it.1 answer -
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Do 8 and 9 and wtite the whole solution ASAP
\( y=e \cdot(\cos x) \) \( y=(\sin x)^{7 x}= \) drgument2 answers -
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7. Compute \( D_{\vec{u}} f\left(x_{0}, y_{0}\right) \) for the following functions in the given direction at the specified point a) \( f(x, y)=3 x y^{2}-6 x^{2}+y-2, \vec{v}=2 i-3 j,(1,2) \). b) \( f2 answers -
2 answers
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II.
Evaluate the integral using the Fundamental Theorem of the Line Integral a) soft curve from \( (0,0) \) to \( (3,8) \) b) soft curve frome \( (0,-\pi) \) to \( (3 \pi / 2, \pi / 2) \) II: Evalúe el2 answers -
2 answers
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Let \( D=[0,1] \times[0,1]=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} \). Evaluate \( \iint_{D} 2 x^{3} e^{y x^{2}} d A \)2 answers -
2 answers
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2 answers
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2 answers
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Use logarithmic differentiation to find \( y^{\prime} \). \[ y=\frac{\sqrt{7-9 x}\left(x^{2}+2\right)^{2}}{x^{2}+5 x+5} \] \[ y^{\prime}= \]2 answers -
Given \( y=f(u) \) and \( u=g(x) \), find \( d y / d x=f^{\prime}(g(x)) g^{\prime}(x) \). 7) \( y=\frac{4}{u^{2}}, u=4 x-3 \)2 answers -
Encontrar la derivada de las siguientes expresiones. \( \frac{d}{d x} \ln \sin x \) \( \frac{d}{d x} \cos ^{-1}(2 x) \) d. \( \frac{d}{d x}\left(\cos ^{-1}(\sin x)\right) \)2 answers -
2 answers
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II. Determine el área de superficie para \( f(x, y)=13+x^{2}-y^{2} \) sobre la región \( R=\left\{(x, y) ; x^{2}+y^{2} \leq 4\right\} \)2 answers -
For the given parametric equations, find the points \( (x, y) \) corresponding to the parameter values \( t=-2,-1,0,1,2 \). \( x=3 t^{2}+3 t, \quad y=2^{t+1} \) \( t=-2 \quad(x, y)=(\quad) \) \( t=-12 answers -
solve problem 12
\( 9-20 \) Find the exact length of the curve. 9. \( y=1+6 x^{3 / 2}, \quad 0 \leqslant x \leqslant 1 \) 10. \( 36 y^{2}=\left(x^{2}-4\right)^{3}, \quad 2 \leqslant x \leqslant 3, \quad y \geqslant 02 answers -
In exercises \( 29-32 \), evaluate the triple integral \( \iiint_{B} f(x, y, z) d V \) over the solid \( B \). 30. \( f(x, y, z)=1-\sqrt{x^{2}+y^{2}+z^{2}}, B=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \2 answers -
2 answers
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7. If \( y=6 x^{5}-2 x^{2}+9 x-3 \) find: a) \( y^{\prime} \) b) \( y^{\prime \prime} \) c) \( y^{\prime \prime \prime} \) d) \( \frac{d y}{d x} \) e) \( \frac{d^{2} y}{d x^{2}} \) f) \( \frac{d^{3} y2 answers -
Find \( \frac{d y}{d x} \) 1. \( y=e^{-5} x^{2} \) 2] \( y=x^{3} e^{x} \) \[ 3 y=e^{1 / x} \] \[ 4 y=e^{\operatorname{xtan} x} \] 10] \( y=p^{\sin x} \) \[ \text { 5] } y=\frac{e^{x}}{\ln x} \] 9] \(2 answers