Calculus Archive: Questions from August 01, 2023
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Find the domain of the function of two variables. Points: 2 10) \( f(x, y)=\sqrt{y+7 x} \) A) \( \{(x, y) \mid y \geq 7 x\} \) B) \( \{(x, y) \mid y z-7 x\} \) C) \( \{(x, y) \mid y \leq 7 x\} \) D) \2 answers -
Problem1. Express in the form \( y=f(x) \) by eliminating the parameter. 1. \( x=t+3, y=4 t \) 2. \( x=e^{-2 t}, y=6 e^{4 t} \) 3. \( x=\ln t, y=2-t \)2 answers -
rentiate the function \( f(x)=\ln \left(\frac{e^{8 x}+1}{e^{2 x}+1}\right) \) \[ \begin{array}{l} \frac{8 e^{8 x}}{e^{8 x}+1}-\frac{2 e^{2 x}}{e^{2 x}+1} \\ \frac{e^{8 x}}{e^{8 x}+1}+\frac{e^{2 x}}{e^2 answers -
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\( \begin{array}{l}\vec{x}=\overrightarrow{2 i}+\vec{j}+\vec{k}, \vec{y}=3 \vec{i} \text { and } \vec{z}=\vec{i}+\vec{j}+3 \vec{k} \text {. Determine } \\ \vec{x}-\vec{y}+2 \vec{z} \text {. } \\ \quad2 answers -
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Compute \( \iint_{\mathcal{S}} f(x, y, z) d S \) for the surface \( y=4-z^{2}, 0 \leq x \leq 2,0 \leq z \leq 2 \) where \( f(x, y, z)=3 z \).2 answers -
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ONLY 36 PLEASE AND THANK YOU.
35-42. Gradient fields Find the gradient field \( \mathbf{F}=\nabla \varphi \) for the following potential functions \( \varphi \). 35. \( \varphi(x, y)=x^{2} y-y^{2} x \) 36. \( \varphi(x, y)=\sqrt{x2 answers -
Evaluate the double integral. \[ \iint_{D} y \sqrt{x^{2}-y^{2}} d A, \quad D=\{(x, y) \mid 0 \leqslant x \leqslant 2,0 \leqslant y \leqslant x\} \]2 answers -
Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=8 y \) and \( x^{2}=4-y \). 1. \( \int_{a}^2 answers -
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Find fx. 16) f(x, y) = x² - y2 x2 + y2
Find \( \mathbf{f}_{\mathbf{x}} \) 16) \( f(x, y)=\frac{x^{2}-y^{2}}{x^{2}+y^{2}} \)2 answers