Calculus Archive: Questions from October 12, 2023
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For \( f(x, y) \), find all values of \( x \) and \( y \) such that \( f_{x}(x, y)=0 \) and \( f_{y}(x, y)=0 \) simultaneously. \[ f(x, y)=x^{2}+3 x y+y^{2}-24 x-21 y+7 \] \[ (x, y)=(\quad) \]1 answer -
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If the function \( f(x, y) \) satisfies the following equations \[ \frac{\partial f}{\partial x}=-\sin y+\frac{1}{1-x y} \quad \text { and } \quad f(0, y)=2 \sin y+y^{3} \] find \( f(x, y) \).1 answer -
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Find \( y^{\prime \prime} \) by implicit differentiation. 15. \( x^{2}+4 y^{2}=4 \) 16. \( \sin y+\cos x=1 \)1 answer -
Given \( f(x, y)=2 x^{5} y-5 x y^{5} \) \[ \begin{array}{l} \frac{\partial^{2} f}{\partial x^{2}}= \\ \frac{\partial^{2} f}{\partial y^{2}}= \end{array} \]1 answer -
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Ejercicios: 1. Evalúe SF-dr donde C está representada por r(t) a) F(x, y) = 3xi + 4yj; C:r(t) = cos(t) i + sen(t)j donde 0 ≤t≤/2 b) F(x, y) = xyti +xzj + yzk; C: r(t) = ti + t2j + 2tk donde 0
Ejercicios: 1. Evalúe \( \int_{c} F \cdot d r \) donde \( C \) está representada por \( r(t) \). a) \[ F(x, y)=3 x i+4 y j ; C: r(t)=\cos (t) i+\operatorname{sen}(t) j \text { donde } 0 \leq t \leq1 answer -
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Esta actividad tiene como propósito ayudar al estudiante a trazar la gráfica de una función básica expandida o comprimida horizontal y verticalmente y a trazar la gráfica de una función que teng1 answer -
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2) Find \( d w / d t \) if \( w=\ln \left(x^{2}+y^{2}+z^{2}\right), x=7 \sin (t), y=6 \cos (t), z=3 \tan (t) \)1 answer -
11. Hallar la solución general del siguiente sistema de EDO por medio del método de los autovectores (caso de raíces complejas). \[ \left\{\begin{array}{l} \frac{d x}{d t}=3 x+2 y \\ \frac{d y}{d t1 answer -
11. Hallar la solución general del siguiente sistema de EDO por medio del método de los autovectores (caso de raíces complejas). \[ \left\{\begin{array}{l} \frac{d x}{d t}=3 x+2 y \\ \frac{d y}{d t1 answer -
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Find all the second partial derivatives. \[ f(x, y)=x^{6} y-2 x^{3} y^{2} \] \[ \begin{array}{l} f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]1 answer -
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Suppose \( f(x, y)=x y^{2}-6 \). Compute the following values: \[ \begin{array}{r} f(-4,-3)= \\ f(-3,-4)= \\ f(0,0)= \\ f(3,-3)= \\ f(t, 5 t)= \\ f(u v, u-v)= \end{array} \]1 answer -
Find dw/dt if w = ln(x² + y² + z²), X = 7sin(t), y = 6cos (t), z = 3tan(t)
Find \( d w / d t \) if \( w=\ln \left(x^{2}+y^{2}+z^{2}\right), x=7 \sin (t), y=6 \cos (t), z=3 \tan (t) \)1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{9} y^{4}+6 x^{4} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]1 answer -
Find the first partial derivatives of the function. \[ f(x, y, z, t)=\frac{x y^{4}}{t+5 z} \] \[ f_{x}(x, y, z, t)= \] \[ f_{y}(x, y, z, t)= \] \[ f_{z}(x, y, z, t)= \] \[ f_{t}(x, y, z, t)= \]0 answers -
Solve the differential equation. \[ \begin{array}{c} y^{\prime}=2 x-y \\ -\ln |y|-x^{2}+c \end{array} \]1 answer -
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numbers 45 and 50 please
39-50 Use logarithmic differentiation to find the derivative of the function. 39. \( y=\left(x^{2}+2\right)^{2}\left(x^{4}+4\right)^{4} \) 40. \( y=\frac{e^{-x} \cos ^{2} x}{x^{2}+x+1} \) 41. \( y=\sq1 answer -
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Calculate the double integral. \[ \iint_{R}\left(30 x^{2} y^{3}-25 y^{4}\right) d A, R=\{(x, y) \mid 0 \leq x \leq 1,0 \leq y \leq 1\} \]1 answer -
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1. For each equation, find \( \frac{d y}{d x} \) : (a) \( y=\sin \left(\sec ^{2}\left(x^{3}\right)\right) \) (c) \( \sin y=e^{x y} \) (b) \( y=\frac{e^{-x} \sin \left(x^{2}+e^{x}\right)}{x^{2} \cos \s1 answer -
Problema4. Calcular el área y la altura de un paralelogramo cuya base está dada por el vector B = i +2j +5k y uno de sus lados por el 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 \( C=i+3 j-k \)1 answer -
Problemas. Dada las funciones escalares y vectoriales: 4 = x²yz Hallar las derivadas parciales a (A) Əx a (pA) dy A = xi+jxzk δ(φΑ) дz
Problema5. Dada las funciones escalares y vectoriales: \[ \varphi=\mathrm{x}^{2} \mathrm{yz} \quad A=x i+j-x z k \] Hallar las derivadas parciales \[ \begin{array}{l} \frac{\partial(\varphi A)}{\parti1 answer -
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If \( y=7 \sin ^{-1}(9 x) \), then \( y^{\prime}(x)= \) If \( y=5 \cos ^{-1}(2 x+11) \), then \( y^{\prime}(x)= \) If \( f(x)=9 \cdot \tan ^{-1}(\sin (x)) \), then \( y^{\prime}(x)= \) If \( y=2 \cot1 answer -
TRABAJO: REALIZAR EN HOJAS MILIMETRICAS: 1) INVESTIGAR CADA CONCEPTO 2) 5 DIAGRAMAS SAGITALES, INDICAR FUNCIÓN O RELACIÓN. 3) 2 FUNCIONES CON SU FUNCIÓN INVERSA (GRAFICAS Y ELEMENTOS) 4) 3 TRASLACI0 answers -
Let \( y=3 e^{1 / 2 x}-7 e^{-x} \). (a) Find \( y^{\prime} \). \[ y^{\prime}= \] (b) Find \( y^{\prime \prime} \). \[ y^{\prime \prime}= \] (c) Is \( y \) a solution of \( 2 y^{\prime \prime}+y^{\prim1 answer -
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8. \( \iint_{R}\left(y+x y^{-2}\right) d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 2,1 \leqslant y \leqslant 2\} \)1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-9 y^{\prime \prime}+20 y^{\prime}=0, \] \[ y(0)=1, \quad y^{\prime}(0)=8, \quad y^{\prime \prime}(0)=6 \text {. } \]1 answer -
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19-36 Sketch the region enclosed by the given curves and find its area. 19. y = 12 - x², y = x² - 6 20. y = x², y = 4x - x² 21. x = 2y², x = 4 + y² 22. y =√x-1, x−y=1 23. y = √/2x.y = -x 2
19-36 Sketch the region enclosed by the given curves and find its area. 19. \( y=12-x^{2}, \quad y=x^{2}-6 \) 20. \( y=x^{2}, \quad y=4 x-x^{2} \) 21. \( x=2 y^{2}, \quad x=4+y^{2} \) 22. \( y=\sqrt{x1 answer -
MC Univ. 2022 Find y' 33. y = sin√1 + x² 35. y = 1. cos 2x 1 + cos 2x - 37. y = cot²(sin 0) 39. f(t) = tan(sec(cos t)) 41. y = √√x + √x 43. g(x) = (2r sin rx + n) 34. y = √√√sin(1 + x
Find \( y^{\prime} \) 33. \( y=\sin \sqrt{1+x^{2}} \) 34. \( y=\sqrt{\sin \left(1+x^{2}\right)} \) 35. \( y=\left(\frac{1-\cos 2 x}{1+\cos 2 x}\right)^{4} \) 36. \( y=x \sin \frac{1}{x} \) 37. \( y=\c1 answer