Calculus Archive: Questions from August 09, 2023
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Calculate \\( \\iint_{\\mathcal{S}} f(x, y, z) d S \\) For \\[ x^{2}+y^{2}=4, \\quad 0 \\leq z \\leq 2 ; \\quad f(x, y, z)=e^{-z} \\] \\( \\iint_{\\mathcal{S}} f(x, y, z) d S= \\)4 answers -
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T3 Q9
Given \\( f(x, y)=6 x^{4}+5 x y^{3}-4 y^{2} \\), find the following numerical values: \\[ f_{x}(4,3)= \\] \\[ f_{y}(4,3)= \\]2 answers -
Evaluate \\( \\iiint_{E}(x+y-2 z) d V \\) where \\( E=\\left\\{(x, y, z) \\mid-7 \\leq y \\leq 0,0 \\leq x \\leq y, 02 answers -
T3 Q10
Given \\( f(x, y)=3 x^{5}-4 x y^{6}-5 y^{2} \\) \\[ \\begin{array}{l} f_{x x}(x, y)= \\\\ f_{x y}(x, y)= \\end{array} \\]2 answers -
Given \\( f(x, y)=3 x^{3}-2 x y^{4}+1 y^{2} \\), find the following numerical values: \\[ \\begin{array}{l} f_{x}(3,3)= \\\\ f_{y}(3,3)= \\end{array} \\]2 answers -
Given f(x, y) = 3x² - 6xy + y, find frz(x, y) = fry(x, y) =
Given \\( f(x, y)=3 x^{2}-6 x y^{4}+y^{6} \\), \\[ f_{x x}(x, y)= \\] \\[ f_{x y}(x, y)= \\]2 answers -
T3 Q20
Find the gradient vector field \\( (\\vec{F}(x, y, z)) \\) of \\( f(x, y, z)=\\ln (4 x+3 y+z) \\). \\( \\vec{F}(x, y, z)=\\langle \\)2 answers -
Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln (3x + y + 42). F(x, y, z) =
Find the gradient vector field \\( (\\vec{F}(x, y, z)) \\) of \\( f(x, y, z)=\\ln (3 x+y+4 z) \\). \\[ \\vec{F}(x, y, z)= \\]2 answers -
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Given f(x, y) = 3x³ - 2xy + 1y2, find the following numerical values: fa(3, 3) = f,(3, 3) =
Given \\( f(x, y)=3 x^{3}-2 x y^{4}+1 y^{2} \\), find the following numerical values: \\[ f_{x}(3,3)= \\] \\[ f_{y}(3,3)= \\]2 answers -
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Find the indefinite integral. \\[ \\int\\left(x^{2}+4 x-5\\right)^{2}(2 x+4) d x \\] \\[ \\left(x^{2}+4 x-5\\right)^{3}+C \\] \\[ \\begin{array}{l} 2\\left(x^{2}+4 x-5\\right)^{3}+C \\\\ \\frac{1}{3}\2 answers -
Q5: Find the gradient vector field \\( \\nabla f \\) of \\( \\boldsymbol{f} \\). \\[ \\begin{array}{l} f(x, y, z)=\\sqrt{x^{2}+y^{2}+z^{2}} \\\\ f(x, y, z)=x^{2} y e^{y / z} \\end{array} \\]2 answers -
using the following properties of a twice-differentiable function y=f(x) , select a possible grañh of f.
\\begin{tabular}{|r|r|r|} \\hline \\( \\mathbf{x} \\) & \\( \\mathbf{y} \\) & Derivatives \\\\ \\hline \\( \\mathrm{x}0, y^{\\prime \\prime}2 answers -
Find the most general antiderivative. \\[ \\int\\left(\\frac{\\sqrt{y}}{5}+\\frac{7}{\\sqrt{y}}\\right) d y \\] A. \\( \\frac{2}{15} y^{\\frac{3}{2}}+14 \\sqrt{y}+C \\) B. \\( \\frac{3}{10} y^{\\frac{2 answers -
Find the derivative. \\[ y=\\int_{0}^{\\tan x} \\sqrt{t} d t \\] A. \\( \\sec x \\tan ^{3 / 2} x \\) B. \\( \\sqrt{\\tan x} \\) C. \\( \\frac{2}{3} \\tan ^{3 / 2} x \\) D. \\( \\sec ^{2} x \\sqrt{\\ta2 answers -
2. Hallar la ecuación polar de la curva representada por la ecuación cartesiana. ( 𝑥^2 + 𝑦^2 )^2 = 𝑎^3 𝑥^2
2. Hallar la ecuación polar de la curva representada por la ecuación cartesiana. \\[ \\left(x^{2}+y^{2}\\right)^{2}=a^{3} x^{2} \\]2 answers -
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Evalúe la integral. (16 puntos)
\\( \\int w^{2} \\operatorname{sen}\\left(\\frac{w}{\\pi}\\right) d w \\)2 answers -
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Determine si las series son convergentes o divergentes. Si convergen halle su suma y verifíquelo gráficamente.
\\( \\begin{array}{l}\\sum_{n=0}^{\\infty} \\frac{9}{4}\\left(\\frac{1}{4}\\right)^{n} \\\\ \\sum_{n=0}^{\\infty} \\frac{17}{3}\\left(-\\frac{1}{2}\\right)^{n}\\end{array} \\)0 answers -
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