Calculus Archive: Questions from September 26, 2022
-
2 answers
-
0 answers
-
0 answers
-
2 answers
-
Given \( f(x, y)=10 \sqrt{5 x^{3}+6 y+8 x y^{4}} \), fir \[ f_{x}(x, y)=\frac{5\left(15 x^{2}+8 y^{4}\right)}{\sqrt{15 x^{3}+6 y+8 x y^{4}}} \times \] \[ f_{y}(x, y)=\sqrt{\frac{5\left(32 x y^{3}+6\ri2 answers -
2 answers
-
\( \begin{array}{ll}\frac{d y}{d x}=x \cdot e^{x-y(x)}, & y(0)=0 \\ \frac{d y}{d x}+\frac{y(x)}{x+1}=6 x, & y(0)=1\end{array} \)2 answers -
find the exact length of the curve. 8, 10, 11
(8. \( y^{2}=4(x+4)^{3}, \quad 0 \leqslant x \leqslant 2, \quad y \) 9. \( y=\frac{x^{3}}{3}+\frac{1}{4 x}, \quad 1 \leqslant x \leqslant 2 \) 10. \( x=\frac{y^{4}}{8}+\frac{1}{4 y^{2}}, \quad 1 \leqs2 answers -
find the derivative solve all please
13. \( y=x^{2} e^{-3 x} \) 14. \( f(t)=t \sin \pi t \) 15. \( f(t)=e^{a t} \sin b t \) 16. \( g(x)=e^{x^{2}-x} \) 17. \( f(x)=(2 x-3)^{4}\left(x^{2}+x+1\right)^{5} \) 18. \( g(x)=\left(x^{2}+1\right)^2 answers -
Considere \( w=x y \cos (z), x=t, y=t^{2} \& z=\arccos (t) \) para determinar \( \frac{\partial w}{\partial t} \)1 answer -
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 -
2 answers
-
For \( f(x, y)=x^{2} y^{4}-3 x^{4} y \), calculate \( f_{x x x}(x, y) \) \[ \begin{array}{l} f_{x x x}(x, y)=3 x y \\ f_{x x x}(x, y)=12 x^{2} y \\ f_{x x x}(x, y)=-72 x y \\ f_{x x x}(x, y)=-3 x y \\2 answers -
Find the second derivative of \( g(x)=4 e^{2 x} \cos (3 x) \). \( -20 e^{2 x} \cos (3 x)-48 e^{2 x} \sin (3 x) \) \( 12 e^{2 x} \cos (3 x)-16 e^{2 x} \sin (3 x) \) \( -144 \cos (3 x) \) \( 144 \sin (32 answers -
2 answers
-
1 answer
-
Find all the second partial derivatives. \[ f(x, y)=x^{7} y^{7}+3 x^{5} y \] \( f_{X X}(x, y)= \) \[ f_{X y}(x, y)= \] \( f_{y x}(x, y)= \) \[ f_{y y}(x, y)= \]2 answers -
1 answer
-
Find \( x, y, z \), and \( w \). \[ \left[\begin{array}{ccc} x & y & (x+5) \\ z & 8 & 8 y \end{array}\right]=\left[\begin{array}{ccc} (2 x-1) & -1 & w \\ x & (9+y) & -8 \end{array}\right] \]2 answers -
Find the quadratic approximation to \[ f(x, y)=\cos (x-y)+2 \sin (x-y) \] \( P(0,0) \) 1. \( Q(x, y)=1+2 x-2 y-\frac{1}{2} x^{2}-x y-\frac{1}{2} y^{2} \) 2. \( Q(x, y)=1-2 x+2 y-\frac{1}{2} x^{2}+x y-2 answers -
Find the quadratic approximation to \[ f(x, y)=\sqrt{1-4 x-2 y} \] at \( P(0,0) \) 1. \( Q(x, y)=1+2 x-y+2 x^{2}-2 x y+y^{2} \) 2. \( Q(x, y)=1-2 x-y-2 x^{2}+2 x y-\frac{1}{2} y^{2} \) 3. \( Q(x, y)=12 answers -
Find the quadratic approximation to \[ f(x, y)=\ln \left(1-4 x^{2}+2 y\right) \] \( P(0,0) \) 1. \( Q(x, y)=2 y-4 x^{2}+2 y^{2} \) 2. \( Q(x, y)=2 x-2 x^{2}+4 y^{2} \) 3. \( Q(x, y)=1+2 y-2 x^{2}+4 y^2 answers -
Find the quadratic approximation to \[ f(x, y)=e^{-x+2 y^{2}} \] \( P(0,0) \) 1. \( Q(x, y)=1+2 y+2 x y+\frac{1}{2} y^{2} \) 2. \( Q(x, y)=1-2 x+\frac{1}{2} x^{2}-2 y^{2} \) 3. \( Q(x, y)=1-x+\frac{1}2 answers -
Es Ecuaciones diferenciales
2. Determine cual o cuales de las siguientes funciones es (son) solución (es) de la ecuación diferencial \( y^{\prime \prime}-9 y=18 \) a. \( y=0 \) b. \( y=2 \) c. \( y=2 x \) d. \( y=2 x^{2} \) e.2 answers -
Interpret the following statement and write it as a differential equation: "The slope of the tangent line at the point p(x,y) is the square of the distance from p(x,y) to the origin."
3. Interprete el siguiente enunciado y escribalo como una ecuación diferencial: "La pendiente de la recta tangente en el punto \( p(x, y) \) es el cuadrado de la distancia desde \( p(x \), y) al orig2 answers -
1 answer
-
4. Compruebe que la familia \( y^{2}-2 y=x^{2}-x+c \) es una solución implícita de la ecuación diferencial \( (2 y-2) y^{\prime}=2 x-1 \)2 answers -
2 answers
-
e derivative of \( y=\frac{3 x^{5}-7 x^{2}-4}{x^{2}} \) \( y^{\prime}=9 x^{-2}+8 x^{-3} \) \( y^{\prime}=9 x^{2}+8 x^{-3} \) \( y^{\prime}=9 x^{2}+8 x^{3} \) \( y^{\prime}=18 x^{2}+8 x^{-3} \)2 answers -
2 answers
-
Calculate the Double integral
28. \( \iint_{R}\left(y+x y^{-2}\right) d A, \quad R=\{(x, y) \mid 0 \leqslant x \leqslant 2,1 \leqslant y \leqslant 2\} \)1 answer -
Find all the second partial derivatives. \[ f(x, y)=x^{6} y^{4}+9 x^{6} y \] \( f_{X X}(x, y)= \) \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \]2 answers -
2. Let \( f(x, y)=\frac{y^{2}}{x+3 y} \). Compute \( f_{x}(4,-1), f_{y}(4,-1) \) and \( f_{x y}(4,-1) \).1 answer -
Math141Q5
Find all points \( (x, y) \) where \( f(x, y) \) has a possible relative maximum or minimum. 5. \( f(x, y)=3 x^{2}+8 x y-3 y^{2}-2 x+4 y \)2 answers -
Math141Q11
Find all points \( (x, y) \) where \( f(x, y) \) has a possible relative maximum or minimum. \( f(x, y)=2 x^{3}+2 x^{2} y-y^{2}+y \)2 answers -
2 answers
-
only answers needed
\( \int \frac{3}{x\left(x^{2}+1\right)^{2}} d x= \) \( \int \frac{\cos y d y}{\sin ^{2} y+3 \sin y-4} \) \( \int \frac{\cos y d y}{\sin ^{2} y+3 \sin y-4}=\frac{2}{5} \ln \left|\tan \left(\frac{y}{2}1 answer -
0 answers
-
Question 14 1 pts \( \tan x \cdot \frac{d y}{d x}+y=\sec x \) \[ \begin{array}{l} y \cdot \cos x=x+C \\ y \cdot \sin x=A x+C \\ y \cdot \sin x=x+C \\ y=x \cdot \sin x+C \end{array} \]2 answers