Calculus Archive: Questions from October 29, 2022
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Differentiate: \[ F(y)=\left(\frac{1}{y^{2}}-\frac{-6}{y^{4}}\right)\left(y-4 y^{3}\right) \] \[ F^{\prime}(y)= \]2 answers -
#10. \( \iiint_{E} e^{\frac{z}{y}} d V \), where \[ E=\{(x, y, z) \mid 0 \leq y \leq 1, y \leq x \leq 1,0 \leq z \leq x y\} \]2 answers -
7 answers
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Find the general solution los each of the follawing equatiqus. Where \( D=\frac{d}{d x} \) 1) \( \left(D^{3}-2 D^{2}-3 D\right) y=0 \) 2) \( \left(D^{2}+D-6\right) \quad y=0 \) 3) \( \left(D^{3}-3 D^{2 answers -
If \( f(x)=\frac{2 e^{3 x}-7 e^{-3 x}}{5 e^{3 x}+4 e^{-3 x}} \) then \( y=\frac{2}{5} \) and \( y=-\frac{7}{4} \) are horizontal asymptote a) True b) False2 answers -
I) \( F \) ind the general solution 1) \( \left(D^{2}-1\right) y=\sin x \) 2) \( \quad\left(D^{2}+9\right) y=\cos 3 x \) 3) \( \left(D^{3}-3 D-2\right) y=x^{3} e^{-x} \) 4) \( y^{\prime \prime}-2 y+y=2 answers -
Homemark \( \# 6 \) Find the general solution 1) \( \left(D^{2}-1\right) \quad y=e^{2 x} \) 2) \( \left(D^{2}-1\right) y=e^{x} \) 3) \( (D-1)^{3}\left(D^{2}+1\right) y=e^{x} \) 4) \( \left(4 D^{2}-122 answers -
2 answers
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Differentiate: (9 pts) 7. \( y=10 e^{7 x} \) 8. \( y=x e^{x^{2}} \) 9. \( y=(\sqrt{x}+1) e^{-2 x} \)2 answers -
Let \( f(x, y)=x^{2}+y^{2} \) a) Find all extrema or saddle points. b) Maximize \( f(\mathrm{x}, \mathrm{y}) \) on \( x^{4}+y^{4} \leq 2 \)2 answers -
2 answers
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Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y^{6}+7 x^{4} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Find y'
Find \( y^{\prime} \) where \( y=6 \sin ^{-1}(\cos (18 x))-\tan ^{-1}(7 x) \) Answer: \[ \begin{aligned} y^{\prime} &=-\frac{108 \sin (18 x)}{\sqrt{1-\cos ^{2}(18 x)}}-\frac{7}{1+49 x^{2}} \\ y^{\prim2 answers -
Find y'
Find \( y^{\prime} \) where \( y=\sin ^{19} x+e^{\cos (15 x)} \) Answer: \[ \begin{array}{l} y^{\prime}=19 \sin ^{18} x \cos x+15 e^{\cos (15 x)} \sin (15 x) \\ y^{\prime}=19 \sin ^{18} x \cos x-e^{\c2 answers -
2 answers
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2. Find all possible critical numbers of the function \( f(x)=\cos ^{2} 2 x-\sin 2 x \quad x \in(0,2 \pi) \).2 answers -
Select the domain of the given function. \[ \begin{aligned} f(x, y, z) &=\frac{10 z x}{\sqrt{2-x^{2}-y^{2}-z^{2}}} \\ \text { Domain } &=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \leq 2\right\} \\ \text2 answers -
Halle todos los valores de equilibrio y utilice el Criterio de Estabilidad Local para determinar si cada equilibrio es localmente estable o inestable. \[ y^{\prime}=2 y \cos y, \quad 02 answers -
Verifique que \( y=\operatorname{sen} x \cos x-\cos ^{2} x \) es solución del problema de valor inicial. \[ 2 y+y^{\prime}=2 \operatorname{sen}(2 x)-1, y\left(\frac{\pi}{4}\right)=0 \]2 answers -
Evaluate the double integral. \[ \iint_{D}(2 x+y) d A, \quad D=\{(x, y) \mid 1 \leq y \leq 4, y-3 \leq x \leq 3\} \]2 answers -
Halle la solución de la ecuación diferencial que satisface la condición inicial dada. \[ y\left(1+x^{2}\right) y^{\prime}-x\left(1+y^{2}\right)=0, y(0)=\sqrt{3} \]2 answers -
Find the partial derivatives of the function \[ \begin{array}{l} f(x, y)=x y e^{8 y} \\ f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \]2 answers -
5. Differentiate the following: a) \( \left.y=e^{x}\left(x^{3}+4\right)\right] \) d) \( f(x)=e^{-4 x} \) b) \( y=x^{3} e^{x} \) e) \( g(x)=e^{x^{3}+8 x} \) \( y=\frac{e^{x}}{x^{2}} \) f) \( h(x)=e^{\s1 answer -
Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-12 y^{\prime \prime}+32 y^{\prime}=84 e^{x} \] \[ \begin{array}{l} y(0)=29, \quad y^{\prime}(0)=25, \quad y^{\prime \prime}(0)=19 \2 answers -
2 answers
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4 and 8 please!
In Exercises 3-20, identify and determine the nature of the critical points of the given functions. 3. \( f(x, y)=2 x y-2 x^{2}-5 y^{2}+4 y-3 \) 4. \( f(x, y)=\ln \left(x^{2}+y^{2}+1\right) \) 5. \( f3 answers -
2 answers
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2 and 16!!
Tangent Planes for Surfaces which are Graphs In Exercises 1-18, find find an equation for the tangent plane to the graph of \( z=f(x, y) \) at the point \( P_{0}= \) \( \left(x_{0}, y_{0}\right) \) 1.2 answers -
2 answers
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2 answers