Calculus Archive: Questions from August 03, 2023
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8. Solve the differential equation. \[ y^{\prime}=x e^{-\sin x}-y \cos x \] a. \( y=\left(\frac{1}{2} x^{2}+C\right) e^{-\sin x} \) b. \( y=\frac{1}{2} x+C e^{-\cos x} \) c. \( y=C e^{-\sin x} \) d. \2 answers -
diffrentiate these
(c) \( y=\cos ^{4}\left(\sin ^{3} x\right) \) (d) \( y=\frac{e^{u}-e^{-u}}{e^{u}+e^{-u}} \) (e) \( \quad y=\ln |\cos (\ln x)| \) (f) \( y=\sqrt{x} e^{x^{2}-x}(x+1)^{\frac{2}{3}} \) (g) \( \quad y=\tan2 answers -
2 points Part 1 of 2 Let \( \vec{F}(x, y, z)=z^{2} \hat{\imath}+2 y \hat{\jmath}+2 x z \hat{k} \). Consider the line integral \[ \int_{C} \vec{F}(x, y, z) \cdot d \vec{r} \] Let \( f(x, y, z)=x z^{2}+2 answers -
0. [-/0.6 Points] SCALCET8 12.3.007. Find \( \mathbf{a} \cdot \mathbf{b} \). \[ \mathbf{a}=7 \mathbf{i}+\mathbf{j}, \quad \mathbf{b}=\mathbf{i}-3 \mathbf{j}+\mathbf{k} \]2 answers -
Part 1 of 2 Let \( \vec{F}(x, y, z)=z^{2} \hat{\imath}+2 y \hat{\jmath}+2 x z \hat{k} \). Consider the line integral \[ \int_{C} \vec{F}(x, y, z) \cdot d \vec{r} \] Let \( f(x, y, z)=x z^{2}+y^{2}+3 \2 answers -
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Find the derivative of the function. Simplify if possible. y = √5 arctan(x) y' =
Find the derivative of the function. Simplify if possible. \[ y=\sqrt{5 \arctan (x)} \] \[ y^{\prime}= \]2 answers -
INTEGRATING FACTOR
RESOLVE ODE WITH INTEGRATING FACTOR: Use \( \int M(x, y) d x \) or \( \int N(x, y) d y \). \[ x \frac{d y}{d x}-y=x^{3}+3 x^{2}-2 x \] \[ \frac{d y}{d x}+y=2+2 x \] \[ \frac{d i}{d t}-6 i=10 \operator2 answers -
9. \( q(x, y)=\sqrt{x}+\sqrt{4-4 x^{2}-y^{2}} \) 10. \( g(x, y)=\ln \left(x^{2}+y^{2}-9\right) \) 11. \( g(x, y)=\frac{x-y}{x+y} \) 12. \( g(x, y)-\frac{\ln (2-x)}{1-x^{2}-y^{2}} \) 13. \( p(x, y)-\fr0 answers -
Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ y=2-z^{2}, \quad 0 \leq x, z \leq 9 ; \quad f(x, y, z)=z \] \( \iint_{S} f(x, y, z) d S= \)2 answers -
f(x, y) = x²/(1+ y²) (a) f(-8, 0) (b) f(14, 1) (c) * ( 12/1₁ - 12/1) (d) f(-4, y)
\[ f(x, y)=x^{2} /\left(1+y^{2}\right) \] (a) \( f(-8,0) \) (b) \( f(14,1) \) (c) \( f\left(\frac{1}{2},-\frac{1}{2}\right) \) (d) \( f(-4, y) \)2 answers -
Find the first partial derivatives of the function. 9(x - y) x + y f(x, y) fx(x, y) = fy(x, y) = =
Find the first partial derivatives of the function. \[ f(x, y)=\frac{9(x-y)}{x+y} \] \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]2 answers -
Find the first partial derivatives of the function. f(x, y, z) = xz - 7x4y7z7 fx(x, y, z) = = fy(x, y, z) = fz(x, y, z) = =
Find the first partial derivatives of the function. \[ t(x, y, z)=x z-7 x^{4} y^{7} z \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \]2 answers -
f(x, y, z, t) = xy²z4t⁹ fx(x, y, z, t) = fy(x, y, z, t) = f₂(x, y, z, t) = ft(x, y, z, t) =
\( f(x, y, z, t)=x y^{2} z^{4} t^{9} \) \( f_{x}(x, y, z, t)= \) \( f_{y}(x, y, z, t)= \) \( f_{z}(x, y, z, t)= \) \( f_{t}(x, y, z, t)= \)2 answers -
Find all the second partial derivatives. f(x, y) = x9y⁹ + 2x5y 9,9 fxx(x, y) = fxy(x, y) = fyx(x, y) = fyy(x, y) =
Find all the second partial derivatives. \[ f(x, y)=x^{9} y^{9}+2 x^{5} y \] \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
please show all steps for # 1,5,9,13 and 17
1-54 Use the guidelines of this section to sketch the curve. 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 3. \( y=x^{4}-4 x \) 4. \( y=x^{4}-8 x^{2}+8 \) 5. \( y=x(x-4)^{3} \) 6. \( y=x^{1 answer -
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please show all steps for #39,43,47
1-54 Use the guidelines of this section to sketch the curve. 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 3. \( y=x^{4}-4 x \) 4. \( y=x^{4}-8 x^{2}+8 \) 5. \( y=x(x-4)^{3} \) 6. \( y=x^{2 answers -
please show all work for #27,31,35
1-54 Use the guidelines of this section to sketch the curve. 1. \( y=x^{3}+3 x^{2} \) 2. \( y=2 x^{3}-12 x^{2}+18 x \) 3. \( y=x^{4}-4 x \) 4. \( y=x^{4}-8 x^{2}+8 \) 5. \( y=x(x-4)^{3} \) 6. \( y=x^{2 answers -
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Find the derivative of the following function. \[ y=\frac{x}{e^{(8 x)}+2} \] \( y^{\prime}=\frac{2+e^{(8 x)}-8 x \cdot e^{(8 x)}}{\left(e^{(8 x)}+2\right)^{2}} \) b. \( y^{\prime}=\frac{2+e^{(8 x)}-82 answers -
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Find the first partial derivatives of the function. \[ f(x, y, z)=x^{2} y z^{3}+8 x y-2 z \] \[ f_{x}(x, y, z)= \] \[ f_{y}(x, y, z)= \] \[ f_{z}(x, y, z)= \] /3.12 Points] SAPCALCBR1 7.2.032. Find th2 answers