Calculus Archive: Questions from September 13, 2023
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D Question 8 Differentiate y F 7 5 131 212 +221 +2678 x1.2 y' = -8.4x^-2.2-10.5x^-1.1 O y'= 8.4x^-0.2 + 10.5x^-3.1 O y'= 8.4x^-0.2 - 10.5x^-1.1 O y'= 8.4x^-2.2 - 10,5x^-3.1 10 5x^-3.1
ferentiate \( y=\frac{7}{x^{1.2}}+\frac{5}{x^{2.1}}+\frac{131}{2678} \) \[ y^{\prime}=-8.4 x^{\wedge}-2.2-10.5 x^{\wedge}-1.1 \] \[ y^{\prime}=8.4 x^{\wedge}-0.2+10.5 x^{\wedge}-3.1 \] \[ y^{\prime}=81 answer -
2. Los gansos salvajes son conocidos por su mala educación. Un ganso vuela hacia el norte a una altitud uniforme de \( h_{g}=30,0 \mathrm{~m} \) sobre una carretera norte-sur, cuando ve un auto delan1 answer -
1. Sketch the following (if possible): (a) y = 3.4 (b) y = -3.4° (c) y = -3.4°
1. Sketch the following(if possible): (a) \( y=3.4^{x} \) (b) \( y=-3.4^{x} \) (c) \( y=-3 \cdot 4^{x} \)1 answer -
\( \begin{array}{l}\text { If } z=f(x, y) \text { and } x=u^{2}-v^{2}, y=2 u v \\ z_{u u}+z_{v v}=4\left(u^{2}+v^{2}\right)\left(z_{x x}+z_{y y}\right)\end{array} \)1 answer -
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3. Solve the given homogeneous equations with IVPs. (a) \( y^{\prime \prime}+y^{\prime}-6 y=0, y(0)=3, y^{\prime}(0)=1 \) (b) \( y^{\prime \prime \prime}-3 y^{\prime \prime}+4 y=0, y(0)=1, y^{\prime}(1 answer -
3. Solve the I.V.P \[ \left(1-\frac{3}{x}+y\right) d x+\left(1-\frac{3}{y}+x\right) d y=0, \quad y(2)=7 \]1 answer -
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Find the Derivative of the following: \[ y=8^{4 x} \] A. \( y^{\prime}=4(\ln 8)\left(8^{4 x}\right) \) B. \( y^{\prime}=4 \ln 8 \) C. \( y^{\prime}=4\left(8^{4 x}\right) \) D. \( y^{\prime}=4 x\left(81 answer -
\[ y=x^{8}, 0 \leq x \leq 1 \] A) \( \int_{0}^{1} \sqrt{1+8 x^{14}} d x \) B) \( \int_{0}^{1} \sqrt{1+64 x^{14}} d x \) C) \( \int_{0}^{1} \sqrt{1+8 x^{7}} d x \) D) \( \int_{0}^{1} \sqrt{1+64 x^{16}}1 answer -
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Please write down the steps, thank you!(a) y" - 2y' - 3y = 3x + 6. Solution: Yp = ax + b. (b) y" - 4y = 5e". Solution: p = ae". (c) y" - 4y = 5e²x. Solution: yp= axe²x. (d) y" - 6y' +9y = 2e³x. S
(a) \( y^{\prime \prime}-2 y^{\prime}-3 y=3 x+6 \). Solution: \( y_{p}=a x+b \). (b) \( y^{\prime \prime}-4 y=5 e^{x} \). Solution: \( y_{p}=a e^{x} \). (c) \( y^{\prime \prime}-4 y=5 e^{2 x} \). Solu1 answer -
Find the derivative of \( y=\frac{x^{9}}{x^{7}+2 x+6} \cdot y^{\prime}= \) \[ \begin{array}{l} \frac{2 x^{15}+8 x^{9}+54 x^{8}}{7 x^{6}+2} \\ \frac{2 x^{15}+16 x^{9}+54 x^{8}}{x^{7}+2 x+6} \\ \frac{21 answer -
Evaluate the integral: \[ \int_{0}^{t}\left(3 s \mathbf{i}+15 s^{2} \mathbf{j}+13 \mathbf{k}\right) d s \] Answer : \[ \mathbf{i}+\quad \mathbf{j}+ \] k1 answer -
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Find the partial derivatives of the function \[ f(x, y)=\frac{-2 x-9 y}{4 x-1 y} \] \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]1 answer -
Compruebe que la ecuación diferencial dada es no exacta. (Para la función de "sen()", utilice "sin()". Por ejemplo, "sen(x)" se escribe como "sin(x) \( (-x y \operatorname{sen}(x)+2 y \cos (x)) d x+1 answer -
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Determine un modelo que describa la población de un pais cuando se permite la inmigración con una tasa constante r. \[ \frac{d P}{d t}=k P+r \] \[ \frac{d P}{d t}=k P-r \] \[ \frac{d P}{d t}=k o P \1 answer -
Given \( \mathrm{y}=7 \sin \mathrm{x} \tan \mathrm{x} \), find \( \mathrm{y}^{\prime}\left(\frac{\pi}{3}\right) \). \[ \mathrm{y}^{\prime}\left(\frac{\pi}{3}\right) \] Tries 0/991 answer -
Question 4: Let \( f(x, y)=6 e^{\frac{2 x}{3}} \cos (\pi y) x^{2}+5 \ln (x) \sin (y)+11^{9} \sqrt{y} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{x y}(x, y)= \\ f_{x x}(x, y)= \\ f_{y}(x, y)= \end{array}1 answer -
\[ \text { Given } y=3 \sin x \tan x \text {, find } y^{\prime}\left(\frac{\pi}{3}\right) \text {. } \] \[ y^{\prime}\left(\frac{\pi}{3}\right) \] Tries 3/99 Previous Tries1 answer -
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Compute the second-order partial derivatives of \[ \begin{array}{l} f(x, y)=e^{6 x^{2}+5 y^{2}} \\ \frac{\partial^{2} f}{\partial x^{2}}(x, y)= \\ \frac{\partial^{2} f}{\partial x \partial y}(x, y)= \1 answer -
Let \( f(x, y)=6 e^{\frac{2 x}{3}} \cos (\pi y) x^{2}+5 \ln (x) \sin (y)+11^{9} \sqrt{y} \) \[ \begin{array}{l} f_{x}(x, y)= \\ f_{x y}(x, y)= \\ f_{x x}(x, y)= \\ f_{y}(x, y)= \end{array} \]1 answer -
Differentiate. y' = 3 3 y = √√√x³ + 3x + 2x6
Differentiate. \[ y=\sqrt[3]{x^{3}+3 x+2} \cdot x^{6} \] \[ y^{\prime}= \]1 answer -
Given: \( f(x)=8 \sin (x)+10 \cos (x) \), find \( f^{\prime \prime}\left(\frac{\pi}{6}\right) \) \( -4 \sqrt{3}-5 \) \( -4-5 \sqrt{3} \) \( 4-5 \sqrt{3} \) \( 4+5 \sqrt{3} \) \( -4+5 \sqrt{3} \)1 answer -
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