Calculus Archive: Questions from August 14, 2023
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Q4: \\( \\int e^{x} \\cos 2 x d x= \\) : a) \\( \\frac{2 e^{x} \\sin 2 x+e^{x} \\cos 2 x}{5}+c \\) b) \\( \\frac{3 e^{x} \\sin 3 x+e^{x} \\cos 3 x}{10}+c \\) c) \\( \\frac{2 e^{x} \\sin 3 x+e^{x} \\co2 answers -
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Q6: \\( \\int \\tan ^{5} x \\sec x d x= \\) : a) \\( \\frac{1}{3} \\tan ^{3} x-\\frac{\\tan ^{2} x}{2}+\\tan x+c \\) b) \\( \\frac{1}{5} \\tan ^{5} x-\\frac{2 \\tan ^{3} x}{3}+\\tan x+c \\) c) \\( \\f2 answers -
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(1) Let \\( f(x, y)=x \\cos y \\). (a) Calculate \\( \\nabla f(x, y) \\). (b) If \\( \\vec{u}=\\frac{3}{5} \\vec{\\imath}-\\frac{4}{5} \\vec{\\jmath} \\), find \\( D_{\\vec{u}} f\\left(2, \\frac{\\pi}2 answers -
Evaluate 402703ey4dydxdz3x .
Evaluate \\( \\int_{0}^{4} \\int_{0}^{27} \\int_{\\sqrt[3]{x}}^{3} e^{y^{4}} d y d x d z \\).2 answers -
37074x−x2 9 x2+y2 dydx x =
\\( \\int_{0}^{37} \\int_{x}^{\\sqrt{74 x-x^{2}}} 9 \\sqrt{x^{2}+y^{2}} d y d x= \\)1 answer -
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In Problems 31-36, determine the form of a particular solu. tion for the differential equation. Do not solve. (31.) \\( y^{\\prime \\prime}+y=\\sin t+t \\cos t+10^{t} \\) 32. \\( y^{\\prime \\prime}-y2 answers -
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In Problems 31-36, determine the form of a particular solu. tion for the differential equation. Do not solve. (31.) \\( y^{\\prime \\prime}+y=\\sin t+t \\cos t+10^{t} \\) 32. \\( y^{\\prime \\prime}-y2 answers -
If f(x) = (x² + (x² + 5x + 5x+7)³, then f'(x) E 6x + 75x¹ + 383x³ + 1005x² + 1344x + 735 f'(3)=
If \\( f(x)=\\left(x^{2}+5 x+7\\right)^{3} \\), then \\[ f^{\\prime}(x)=6 x^{5}+75 x^{4}+383 x^{3}+1005 x^{2}+1344 x+735 \\]2 answers -
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Cierta empresa produce y vende televisores de pantalla plana. El ingreso semanal total y el costo en dolares está dado por : \\[ \\begin{array}{c} R(x, y)=-0.2 x^{2}-0.25 y^{2}-0.2 \\mathrm{xy}+225 \2 answers -
SELECCIONE LA RESPUESTA CORRECTA dy dx Resuelva +2xy=0 A B C D E y=ce²² y=e²² +c y=e*² +c y=ce²² y=c₁e¹² + C₂
3. Tres fuerzas que actúan sobre un objeto se proporcionan por \\[ \\vec{F}_{1}=(2.00 \\mathrm{Ni}+2.00 \\mathrm{Nj}), \\quad \\vec{F}_{2}=(5.00 \\mathrm{Ni}-3.00 \\mathrm{Nj}) \\text { y } \\vec{F}_2 answers -
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Let And show that the function: Is continuous on the point (1, 2)
\( f(x, y)=\frac{2(x-1)(y-2)}{\sqrt{(x-1)^{2}+(y-2)^{2}}}+\frac{3 x y}{\sqrt{2 x^{2}+5 y^{2}}} \) \( \widetilde{f}(x, y)=\left\{\begin{array}{c}f(x, y), \\ \frac{6}{\sqrt{22}},(x, y)=(1,2)\end{array}2 answers