Calculus Archive: Questions from October 28, 2022
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2 answers
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\[ f(x, y)=\frac{x}{\sqrt{4-x^{2}-y^{2}}} \] The domain of \( f \) is equal to \[ \begin{array}{l} \left\{(x, y) \in \mathbb{R}^{2} \mid x^{2}+y^{2}4\right\} \end{array} \] \[ \left\{(x, y) \in \mathb2 answers -
Answer all questions please.
Q3. Find \( \frac{d y}{d x} \), i) \( y=\ln \left(\cos ^{-1}(x)\right) \) ii) \( y=\left(x^{2}+1\right)^{\sin (x)} \) iii) \( y=\left(x^{3}+\sqrt[3]{x}\right) 5^{x} \)2 answers -
27-34 Calculate the double integral. 29. \( \iint_{R} \frac{x y^{2}}{x^{2}+1} d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 1,-3 \leqslant y \leqslant 3\} \)2 answers -
Given \( f(5)=3, f^{\prime}(5)=3 x+7 \) \( g(5)=2 x-1, g^{\prime}(5)=\frac{1}{2} \) If \( h(t)=f(t) \cdot g(t) \), find \( h^{\prime}(5) \)2 answers -
Consideremos el solido \( \left\{(x, y, z): x^{2}+y^{2} \leq 1,0 \leq z \leq 3-x^{2}-y^{2}\right\} \) 1. El volumen es \( 6 \pi \) 2. El volumen se puede calcular resolviendo una integral triple cuyo2 answers -
2 answers
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Given \( f(x, y)=\sin (14 x+5 y)+\ln \left(x^{2} y+4 x y\right) \), find \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]2 answers -
2 answers
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Solve the following separable ODEs: (i) \( y^{\prime}+y=1, y(0)=2.5 \) (ii) \( \quad y^{\prime}=2 x y, \quad y(1)=4 \)2 answers -
2 answers
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2 answers
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Let \( f(x, y)=x^{2}+y^{2} \) 1. Find all extrema or saddle points. 2. Maximize \( f(x, y) \) on \( x^{4}+y^{4} \leq 2 \)2 answers -
Sketch the graph of a twice-differentiable function \( \mathrm{y} \mathrm{f}(\mathrm{x}) \) with the properties given in the table. Choose the correct graph below.2 answers -
ALL I ASK IF FOR YOU is TO MAKE IT UNDERSTANDABLE
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 \( z=0, x=0, z=y-7 x \) and \( y=14 \). 1. \( \int_{a1 answer -
2 answers
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Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=\ln (a x+b y) \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
2 answers
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2 answers
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Find \( \sin \left(\frac{x}{2}\right), \cos \left(\frac{x}{2}\right) \), and \( \tan \left(\frac{x}{2}\right) \) from the given information. \( \cot (x)=8, \quad 180^{\circ}2 answers -
Find the partial derivatives of the function \[ f(x, y)=x y e^{7 y} \] \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \]2 answers -
2 answers
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2 answers
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Calcular \( \int f \int_{E} \frac{z}{y+1} d V \) donde \( E=\left\{(x, y, z): 0 \leq y \leq 1,0 \leq z \leq 1,0 \leq x \leq \sqrt[2]{1-z^{2}}\right\} \) 1. La integral se puede calcular \( \iint_{E} \2 answers -
Consider the solid {(2, y, z) : x^2 + y^2 ≤ 1, 0 ≤ z≤3-x^2-y^2} 1. The solid is a cone 2. The volume is 6π 3.The volume is (function in the image)dzdydx 4. Volume is 6 5. Th
Consideremos el solido \( \left\{(x, y, z): x^{2}+y^{2} \leq 1,0 \leq z \leq 3-x^{2}-y^{2}\right\} \) 1. El solido es un cono 2. El volumen es \( 6 \pi \) 3. El volumen es \( \iint_{\left\{(x, y)=x^{22 answers -
Sea \( E=\left\{(x, y, z): 4 \leq x^{2}+y^{2} \leq 9,0 \leq z \leq 5-x-y\right\} \) y calculemos la integral \( \iiint_{E} x d V \) Se puede calcular la integral triple en coordenadas cartesianas o en2 answers -
1. a) b) c) d) e)
Find \( y^{\prime} \) where \( y=\sin ^{16} x+e^{\cos (18 x)} \) \( y=\cos \left(x e^{3 x}\right)-19^{\sec x} \) Find \( y^{\prime} \) where \( y=\frac{16-e^{15 x}}{x+\log _{15^{x}}} \) \( y=\cot \2 answers -
Evaluate each integral. \[ \begin{array}{r} \int_{x-y}^{x+y} y d z= \\ \int_{0}^{x} \int_{x-y}^{x+y} y d z d y= \end{array} \] Now evaluate \( \iiint_{E} y d V \), where \( E=\{(x, y, z) \mid 0 \leq x2 answers -
(1 point) Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=2 x+3 \) and \( R=[2,8] \times[-4,1] \). \[ \iint_{R} f(x, y) d A= \]2 answers -
Multiple Choice:
\( y=9 \sin ^{-1}(\cos (5 x))-\tan ^{-1}(9 x) \) \( \begin{aligned} y^{\prime} &=-45+\frac{9}{1+81 x^{2}} \\ y^{\prime} &=\frac{45}{\sqrt{1-\cos ^{2}(5 x)}}-\frac{9}{1+81 x^{2}} \\ y^{\prime} &=\frac2 answers -
Let \( \mathbf{r}(t)=(\sqrt{t+2}) \mathbf{i}+\left(\frac{t^{2}-4}{t+2}\right) \mathbf{j}+\sin (-2 \pi t) \mathbf{k} \) Then \( \lim _{t \rightarrow 1} \mathbf{r}(t)= \) \( \mathbf{i}+ \) \( \mathbf{j}2 answers -
2 answers
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Find the field lines of the three-dimensional vector functions (a) \( \mathbf{F}(x, y, z)=x y \mathbf{i}+\left(y^{2}+1\right) \mathbf{j}+z \mathbf{k} \). (b) \( \mathbf{F}(x, y, z)=y z \mathbf{i}+x z2 answers