Calculus Archive: Questions from October 02, 2022
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Given \( f(x, y)=5 x^{3} y+9 x y^{2} \) \( \frac{\partial^{2} f}{\partial x^{2}}= \) \[ \frac{\partial^{2} f}{\partial y^{2}}= \]2 answers -
II. Considere \( w=x y \cos (z), x=t, y=t^{2} \& z=\arccos (t) \) para determina \( \frac{\partial w}{\partial t} \)2 answers -
IV.Determine el gradiente de la función y la dirección de máximo crecimiento de la función en el punto dado. \[ f(x, y)=x \tan (y) ; P\left(2, \frac{\pi}{3}\right) \]2 answers -
I. Evalúe el integral cambiando a coordenadas polares a) \( \int_{-1}^{1} \int_{0}^{\sqrt{1-x^{2}}} \cos \left(x^{2}+y^{2}\right) d y d x \) b) \( \int_{0}^{3} \int_{0}^{\sqrt{9-x^{2}}}\left(x^{2}+y^2 answers -
II. Set up and evaluate the integral at the most convenient coordinates to determine the area of the region
II. Establezca y evalúe el integral en las coordenadas más convenientes para determinar el área de la región. A. B.2 answers -
II. Utilice coordenadas polares para escribir y evaluar la integral doble \( \int_{R} \int f(x, y) d A \) Para \( f(x, y)=x+y \) donde \( R: x^{2}+y^{2} \leq 4, x \geq 0, y \geq 0 \)2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{8} y^{7}+2 x^{6} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
Paso por paso
Hallar la derivada de la función \[ f(x)=2^{2}-6(2)-5 \] Calcular la derivada de la función \[ f(x)=3(1)^{3}+2(1)-1 \]0 answers -
1. Let \( f(x, y)=\ln \left(y^{2}+x^{3}\right) \). Compute \( D_{\left\langle\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right\rangle} f(-2,-3) \).2 answers -
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Differentiate and simplify (e)-(k)
(e) \( y=\frac{x}{\sqrt{x^{2}+5}} \) (f) \( h(t)=e^{7 t \sin (2 t)} \) (g) \( g(t)=e^{t \cos (t)} \) (h) \( h(x)=e^{4 x} \sin ^{2}(x)+e^{4} x \cos ^{2}(x) \) (i) \( h(x)=\ln \left(e^{x} \sin ^{2}(x)+e2 answers -
Set up and evaluate the integral at the most convenient coordinates to determine the area of the region
II. Establezca y evalúe el integral en las coordenadas más convenientes para determinar el área de la región.2 answers -
Q14
Find the absolute maxima and minima of \( f(x, y) \) on the given regions (1) \( f(x, y)=x^{2}+y^{2} \) on \( R=\{(x, y) \mid 0 \leq x \leq 1, \quad 0 \leq y \leq 2-2 x\} \) (2) \( f(x, y)=x+x^{2}+2 y2 answers -
Differentiate the following
\( y=\sinh 4 x \) \( y=\cosh ^{3}(8 x+1) \) \( y=\cosh ^{-1}\left(x^{2}\right) \) \( y=\sinh ^{-1}(2 x+1) \)2 answers -
the domain and the range of \( g(x, y, z)=\sqrt{z^{2}-y^{3}-x-18} \). \[ \begin{array}{l} D_{g}=\left\{(x, y, z) \in \mathbb{R}^{3} \mid z^{2}-y^{3}-x-18>0\right\}, R_{g}=(0, \infty) \\ D_{g}=\left\{(2 answers -
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If f(x) = 7√x(x³ - 7√x + 2) please show all steps
If \( f(x)=7 \sqrt{x}\left(x^{3}-7 \sqrt{x}+2\right) \) Find \( f^{\prime}(4) \).2 answers -
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Find the first partial derivatives of the function. \[ h(x, y, z, t)=x^{3} y \cos \left(\frac{z}{t}\right) \] \[ h_{x}(x, y, z, t)= \] \[ h_{y}(x, y, z, t)= \] \[ h_{z}(x, y, z, t)= \] \[ h_{t}(x, y,2 answers -
Find the partial derivatives of the function \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y) \]0 answers -
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{5} y^{6}+3 x^{7} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]2 answers -
7. \( \frac{d y}{d x}=3 e^{x}, \quad y=6 \), when \( x=0 \) 8. \( \frac{d y}{d x}=4 e^{-3 x}, \quad y=2 \), when \( x=0 \). 9. \( \frac{d y}{d x}=4 y, \quad y=3 \), when \( x=0 \). 10. \( \frac{d y}{d2 answers -
differential Equations
s.] \( (x+y-4) d x-(3 x-y-4) d y=0 \), when \( x=3, y=7 \) s.] \( (9 x-4 y+4) d x-(2 x-y+1) d y=0 \)2 answers -
Solve the initial value problem \[ y^{\prime \prime}-20 y^{\prime}+100 y=0, y(0)=0, y^{\prime}(0)=5 \] \[ \begin{array}{l} y=e^{10 t} \\ y=5 e^{10 t}+5 e^{10 t} \\ y=5 t e^{10 t} \\ y=5 e^{10 t} \\ y=2 answers -
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Find \( y^{\prime} \) given the following equation. \[ y=\ln \left(9 x^{2}+5 y^{2}\right) \] \[ y^{\prime}= \]4 answers -
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Evaluate and simplify \( y^{\prime} \). \[ y=8 x^{2} \cos x-16 x \sin x-16 \cos x \] \[ y^{\prime}= \]2 answers -
ve of Algerbraic Functions \( 1+ \) Find \( y^{\prime} \) if \( y=\frac{-13}{\sqrt[3]{x}} \) \[ y^{\prime}= \]2 answers -
Solve the initial value problem \( t^{2} \frac{d y}{d t}-t=1+y+t y, y(1)=2 \). \[ y= \] Solve the initial value problem \( y^{\prime}=4 y^{2} \sin x, y(0)=3 \). \[ y= \]2 answers -
\( f(x, y)=3 x^{4} y^{2}-x^{2} \cos y+4 x^{3}-y^{3} \) 2. For \( g(x, y, z)=x^{3} y^{2} e^{z}-\ln \left(4 x y^{2} z^{3}\right)+6 x y^{3} z^{4} \), find \( \frac{\partial^{3} g}{\partial x \partial y2 answers -
Differientiate
e. \( (4 p t s) \quad y=\ln \left(\frac{1+e^{\pi}}{1-e^{\pi}}\right) \) f. \( (4 p t s) \quad y=\ln \left(\frac{x(x+2)^{4}}{\sqrt{x-1}}\right) \) g. \( (4 p t x) \quad y=\ln \left(\ln x^{2}\right) \)2 answers -
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I need help with y"
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=\sqrt{\sin (x)} \\ y^{\prime}=\frac{\cos (x)}{2 \sqrt{\sin (x)}} \end{array} \]2 answers -
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