Calculus Archive: Questions from July 15, 2022
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Solve the next systems of linear differential equations by elimination theses are the answers. how to solve the problems to get the same answers?
(1) \( \left\{\begin{array}{l}y^{\prime}=3 y+2 z \\ z^{\prime}=3 y-2 z\end{array}\right. \) (2) \( \left\{\begin{array}{l}y^{\prime}=-z \\ z^{\prime}=y\end{array}\right. \) (3) \( \left\{\begin{array}1 answer -
\[ y=1 / x+\tan x \] Find \( y^{\prime} \). \( -x+\sec x \) \( -1 /\left(x^{\wedge} 2\right)+\left(\sec ^{\wedge} 2\right) x \) \( -\left(\sec ^{\wedge} 2\right) x \) Question 21 \( 1 \mathrm{pts} \)1 answer -
Solve the problem. Suppose that \( R=\{(x, y): 0 \leq x \leq 6,0 \leq y \leq 5\} \), \( R_{1}=\{(x, y): 0 \leq x \leq 6,0 \leq y \leq 4\} \), and \( R_{2}=\{(x, y): 0 \leq x \leq 6,4 \leq y \leq 5\} \1 answer -
Find the indicated limit by using the limits \( \lim _{(x, y) \rightarrow(a, b)} f(x, y)=2 \) and \( \lim _{(x, y) \rightarrow(a, b)} g(x, y)=-9 \). \[ \lim _{(x, y) \rightarrow(a, b)} \frac{8 f(x, y)1 answer -
a) Given a function \( f(x, y)=1+\sqrt{\ln \left(y-x^{2}\right)} \). Find: i. the domain of \( f(x, y) \). \( (3 \) marks ii. the range of \( f(x, y) \). (1 mark)1 answer -
please solve!!!
\[ y=\cot (\csc x) \] \[ y=\sqrt{\sin \sqrt{x}} \] \( y=(\cos x)^{x} \) \[ y=\frac{\left(x^{2}+1\right)^{4}}{(2 x+1)^{3}(3 x-1)^{5}} \] \[ y=\ln \left(\arcsin x^{2}\right) \]1 answer -
Determine how the following lines interact. a. \( (x, y, z)=(-2,1,3)+t(1,-1,5) ;(x, y, z)=(-3,0,2)+s(-1,2,-3) \) b. \( (x, y, z)=(1,2,0)+t(1,1,-1) ;(x, y, z)=(3,4,-1)+s(2,2,-2) \) c. \( x=2+t, y=-1+21 answer -
Situation I: Evaluate intewales by presenting all their steps: Situation II: Find the particular solution of the differential equation that satisfy the given conditions.
Situación I: Evalúe las integales presentando todo sus pasos: a) \( \int_{1}^{3}\left(4^{x+1}+2^{x}\right) d x \) b) \( \int_{-2}^{0} \frac{e^{x+1}}{7-e^{x+1}} d x \) Situación II: Encuentre la sol1 answer -
1) Evalúe a) \( \operatorname{csch}(\ln \) (3)) b) \( \cosh (0) \) 2) Presente el procesos pa a) \( f(x)=\frac{x}{6} \operatorname{senh}(3 x) \) b) \( f(x)=\operatorname{sech}^{2}(2 x) \) 3) Evalúe1 answer -
Longitud de arco Establezca y evalúe la integral definida por determinar la longitud del arco de la curva \( y=\frac{x^{4}}{8}+\frac{1}{4 x^{2}} \) en el intervalo \( [2,3] \).1 answer -
Calculate \( y^{\prime}, y^{\prime \prime} \) and \( y^{\prime \prime \prime} \) \[ y=\frac{1}{7-x} \] \( y^{\prime}= \) \( y^{\prime \prime} \)1 answer -
Find all solutions to the equation. \[ x^{3}+512=0 \] Choose the correct solutions. A. \( \left\{4\left(\cos 0^{\circ}+i \sin 0^{\circ}\right), 4\left(\cos 120^{\circ}+i \sin 120^{\circ}\right), 4\lef1 answer -
3 answers
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find dy/dx for both pls
\( y=5^{3 x+1} \ln \left(-3 x^{2}+2 x-3\right) \) \( y=\operatorname{lo} g_{4}^{x(x+1)(2 x-1)} \)3 answers -
1 answer
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Differentiate the function. \[ F(x)=\int_{2 x}^{x^{2}} \sqrt{t} d t, x \geq 0 \] A) \( F^{\prime}(x)=\frac{2}{3} x^{3}-\frac{2}{3}(2 x)^{3 / 2} \) B) \( F^{\prime}(x)=2 x^{2}-2 \sqrt{2 x} \) C) \( F^{3 answers -
Solve all four using the comparison testb
\( \sum_{n=1}^{\infty} \frac{1}{n^{3}+8} \) \( \sum_{n=1}^{\infty} \frac{n+1}{n \sqrt{n}} \) \( \sum_{n=1}^{\infty} \frac{9^{n}}{3+10^{n}} \) \( \sum_{n=1}^{\infty} \frac{1+\cos n}{e^{n}} \)5 answers -
1 answer
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Find the Jacobian of the transformation. \[ x=4 v+4 w^{2}, \quad y=5 w+5 u^{2}, \quad z=7 u+7 v^{2} \] \( \frac{\partial(x, y, z)}{\partial(u, v, w)}= \)1 answer -
220. Suppose \( f(x, y)=x+y, u=e^{x} \sin y, x=t^{2} \), and \( y=\pi t \), where \( x=r \cos \theta \) and \( y=r \sin \theta \). Find \( \frac{\partial f}{\partial \theta} \)3 answers -
Evaluate the integral. \[ \int 7 \sec ^{4} x d x \] A. \( \frac{7}{3} \tan ^{3} x+C \) B. \( -\frac{7}{3} \tan ^{3} x+C \) C. \( 7 \tan x+\frac{7}{3} \tan ^{3} x+C \) D. \( 7(\sec x+\tan x)^{5}+C \)1 answer -
3. (4 pts) Solve \[ \vec{x}^{\prime}=\left[\begin{array}{cc} -5 & -2 \\ 8 & 3 \end{array}\right] \vec{x} \] 4. \( (6 \mathrm{pts}) \vec{x}^{\prime}=\left[\begin{array}{cc}-3 & 0 \\ 0 & -3\end{array}\r1 answer