Calculus Archive: Questions from November 13, 2022
-
Find y' and y''. y = ln(6x) x6 y' = Correct: Your answer is correct. y'' =
Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ \begin{array}{c} y=\frac{\ln (6 x)}{x^{6}} \\ y^{\prime}=\frac{1-6 \ln (6 x)}{x^{7}} \\ y^{\prime \prime}=\frac{13+4 \ln \left(x^{12}\right)}{x^{82 answers -
\[ \int_{0}^{1} \int_{x^{2}}^{x} f(x, y) d y d x=\int_{x^{2}}^{x} \int_{0}^{1} f(x, y) d x d y \] True False2 answers -
find f(1,2,3) given the f(x,y,z)= ________
Halle \( f(1,3,2) \) dado que \( f(x, y, z)=\frac{\sqrt{x^{2}+y}}{z^{2}} \) Seleccione una: a. 1 b. \( \frac{\sqrt{2}}{4} \) C. \( \frac{\sqrt{2}}{2} \) d. \( 1 / 2 \)2 answers -
select one: a. b. c. d.
\[ \lim _{(x, y) \rightarrow(1,3)} \frac{x^{2} y^{2}-9}{x y-3}= \] Seleccione una: a. \( -3 \) b. 0 c. 6 d. 22 answers -
given the f(x,y)=____________, then fx(1,1) + fy(1,1)= answer:____________
Dado que \( f(x, y)=6 x^{2}+5 x^{3} y^{4}-10 y^{5} \), luego \( f_{x}(1,1)+f_{y}(1,1)= \) Respuesta:2 answers -
Dado que \( f(x, y)=x\left(e^{x y}+y\right) \), entonces \( f_{x}(x, y)= \) Seleccione una: a. \( \left(e^{x y}+y\right)+x\left(y e^{x y}\right) \) b. \( x^{3} e^{x y} \) c. \( x^{2} e^{x y}+x \) d. \2 answers -
\[ \lim _{(x, y) \rightarrow(0,0)} \frac{2 x y}{x^{2}+y^{2}}= \] Seleccione una: a. 1 b. \( -1 \) c. No existe d. 02 answers -
2 answers
-
Determine the derivative \( \frac{d y}{d x} \) for each function. (A) \( y=(\sin (\pi x)-\cos (\pi x))^{4} \) (B) \( y=\left(x^{2}+1\right)^{3}(2 x-5) \). (C) \( y=\sin ^{-1}(\sqrt{x}) \). (D) \( 2 x^1 answer -
Find the values of the function. \[ g(x, y)=x^{2} e^{4 y} \] (a) \( g(-4,0) \) (b) \( g\left(4, \frac{1}{4}\right) \)2 answers -
2 answers
-
Find all the second partial derivatives. \[ \begin{array}{c} f(x, y)=x^{4} y^{8}+7 x^{6} y \\ f_{x x}(x, y)=12 x^{2} y^{8}+210 x^{4} y \\ f_{x y}(x, y)=32 x^{3} y^{7}+42 x^{5} \\ f_{y x}(x, y)=32 x^{32 answers -
Analizar y dibujar la gráfica de \( f(x)=x^{4}+2 x^{3}-3 x^{2}-4 x+4 \) respondiendo los siguiente: n) Primera derivada o) Segunda derivada p) Intersecciones con el eje \( x \) q) Intersección con e1 answer -
Solve for \( Y(s) \). \[ y^{\prime \prime}+y^{\prime}-y=t^{3} \] \[ y(0)=1, y^{\prime}(0)=0 \] \[ Y(s)= \]2 answers -
\( f(x)=\left\{\begin{array}{ll}\frac{x^{2}-25}{x+5} & \text { if } x0\end{array}\right. \) A) \( \lim _{x \rightarrow-5} f(x)= \) B) \( \lim _{x \rightarrow 0} f(x)= \) C) \( \lim _{x \rightarrow 5}2 answers -
Determine the global extreme values of the function \( f(x, y)=5 x^{3}-2 y, \quad 0 \leq x, y \leq 1 \) \[ \begin{array}{l} f_{\min }= \\ f_{\max }= \end{array} \]2 answers -
Determine the global extreme values of the function \( f(x, y)=4 x^{3}+4 x^{2} y+y^{2}, \quad x, y \geq 0, x+y \leq 1 \) \[ \begin{array}{l} f_{\min }= \\ f_{\max }= \end{array} \]2 answers -
2 answers
-
XI. Evaluate the integrals b) âˆE 12ð‘¥ð‘¦ð‘§ð‘‘𑉠where E is the region given by 0 ≤ 𑧠≤ 1 0 ≤ 𑦠≤ 1 0 ≤ 𑥠≤ 2
XI. Evalúa las integrales a) \( \int_{0}^{1} \int_{0}^{z} \int_{0}^{2}(2 x-y) d x d y d z \) b) \( \iiint_{E} 12 x y z d V \) donde \( E \) es la región dada por \( 0 \leq z \leq 1 \quad 0 \leq y \l2 answers -
Evaluate ∬ ð‘¦ð‘’^ð‘¥ð‘¦ð‘‘ð´ ð‘… where R is the rectangle 0 ≤ 𑥠≤ 1 0 ≤ 𑦠≤ 2
II. Evalúa \( \iint_{R} y e^{x y} d A \) donde \( R \) es el rectángulo \( 0 \leq x \leq 1 \quad 0 \leq y \leq 2 \)2 answers -
X. Using spherical coordinates evaluates âˆE (ð‘¥^2 + ð‘¦^2+z^2)ð‘‘𑉠where E is the solid between the two spheres ð‘¥^2 + ð‘¦^2 + ð‘§^2 = 1 and ð‘¥^2 + ð‘¦^2 + ð‘§^2 = 4
X. Usando coordenadas esféricas evalúa \( \iiint_{E}\left(x^{2}+y^{2}+z^{2}\right) d V \) donde \( \mathrm{E} \) es el sólido entre las dos esferas \( x^{2}+y^{2}+z^{2}=1 \quad \) y \( \quad x^{2}+2 answers -
Evalúa ∬ (ð‘¥ 2 + 2ð‘¦)ð‘‘ð´ ð‘… donde R es la región acotada por 𑦠= 2𑥠𑦠𑦠= ð‘¥ 2
III. Evalúa \( \iint_{R}\left(x^{2}+2 y\right) d A \) donde \( \mathbf{R} \) es la región acotada por \( y=2 x \) y \( y=x^{2} \)2 answers -
Evaluate ∬ ð‘¦ð‘‘ð´ ð‘… where R is the region bounded by ð‘¥ = 𑦠2 𑦠= 𑥠− 2
IV. Evalúa \( \iint_{R} y d A \) donde \( R \) es la región acotada por \( x=y^{2} \quad y=x-2 \)2 answers -
I. Evaluate the integrals
I. Evalúa las integrales a) \( \int_{0}^{2} \int_{x^{2}}^{4} 4 x y d y d x \) b) \( \int_{0}^{1} \int_{\sqrt{y}}^{1} 2 x d x d y \)2 answers -
Find the volume of the solid below 𑧠= 4 and above the region bounded by 𑦠= 𑥠𑥠= 2 𑦠= 0
V. Halla el volumen del solido que está debajo de \( z=4 \) y sobre la región acotada por \[ y=x \quad x=2 \quad y=0 \]2 answers -
II. Evaluate ∬R ð‘¦ð‘’^ð‘¥ð‘¦ ð‘‘ð´ where R is the rectangle 0 ≤ 𑥠≤ 1 0 ≤ 𑦠≤ 2 III. Evaluate ∬R (ð‘¥^2 + 2ð‘¦)ð‘‘ð´ where R is the region bounded by 𑦠= 2𑥠𑦠ð
II. Evalúa \( \iint_{R} y e^{x y} d A \) donde \( \mathrm{R} \) es el rectángulo \( 0 \leq x \leq 1 \quad 0 \leq y \leq 2 \) I III. Evalúa \( \iint_{R}\left(x^{2}+2 y\right) d A \) donde \( \mathrm2 answers -
2 answers
-
2 answers
-
IV. Evaluate ∬R ð‘¦ð‘‘ð´ where R is the region bounded by ð‘¥ = ð‘¦^2 𑦠= 𑥠− 2 V. Find the volume of the solid below 𑧠= 4 and above the region bounded by 𑦠= ð‘¥ ð‘¥ = 2 ð‘¦
IV. Evalúa \( \iint_{R} y d A \) donde \( \mathrm{R} \) es la región acotada por \( x=y^{2} \quad y=x-2 \) V. Halla el volumen del solido que está debajo de \( z=4 \) y sobre la región acotada por2 answers -
Find the volume of the solid between the planes 𑦠= 1 and 𑦠= 4 and inside the cylinder 𑥠2 + 𑧠2 = 9 using a triple integral in cylindrical coordinates
IX. Halla el volumen del solido entre los planos \( y=1 \) y \( y=4 \) y dentro del cilindro \( x^{2}+z^{2}=9 \) usando una triple integral en coordenadas cilÃndricas2 answers -
Using spherical coordinates evaluates ∠(ð‘¥ 2 + 𑦠2 + 𑧠two )ð‘‘𑉠ð¸ where E is the solid between the two spheres ð‘¥ 2 + 𑦠2 + 𑧠2 = 1 yð‘¥ 2 + 𑦠2 + 𑧠2 = 4
X. Usando coordenadas esféricas evalúa \( \iiint_{E}\left(x^{2}+y^{2}+z^{2}\right) d V \) donde \( \mathrm{E} \) es el sólido entre las dos esferas \( x^{2}+y^{2}+z^{2}=1 \quad \) y \( \quad x^{2}+2 answers -
∠12ð‘¥ð‘¦ð‘§ð‘‘𑉠ð¸ where E is the region given by 0 ≤ 𑧠≤ 1 0 ≤ 𑦠≤ 1 0 ≤ 𑥠≤ 2
b) \( \iiint_{E} 12 x y z d V \) donde \( \mathrm{E} \) es la región dada por \( 0 \leq z \leq 10 \leq y \leq 1 \quad 0 \leq x \leq 2 \)2 answers -
2 answers
-
2 answers
-
2 answers
-
Function Point \( f(x, y)=\ln (x-y) \quad(0,-7) \) \( f_{x x}(0,-7)= \) \( f_{x y}(0,-7)= \) \( f_{y x}(0,-7)= \) \( f_{y y}(0,-7)= \)2 answers -
2 answers
-
2 answers
-
Question 7 (10 points). Find \( y^{\prime} \) and \( y^{\prime \prime} \) a) \( y=\ln \left(x+\sqrt{1+x^{2}}\right) \) b) \( y=\ln (\sec x+\tan x) \) c) \( y=\frac{\ln x}{x^{2}} \) d) \( y=e^{\ln \lef2 answers -
Find all the second partial derivatives. \[ \begin{array}{l} \quad f(x, y)=\ln (a x+b y) \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]4 answers -
Let \( \mathbf{F}(x, y, z)=\sin y \mathbf{i}+(x \cos y+\cos z) \mathbf{j}-y \sin z \mathbf{k} \) and \[ C: \mathbf{r}(t)=\sin t \mathbf{i}+t \mathbf{j}+2 t \mathbf{k}, 0 \leq t \leq \frac{\pi}{2} \tex2 answers -
2 answers
-
2 answers
-
7. Find the rectangular equation if \( r=4 \cos \theta+4 \sin \theta \) (a) \( x^{2}+y^{2}=4 \) (b) \( x^{2}+y^{2}=4(x-y) \) (c) \( x^{2}+y^{2}=4(x+y) \) (d) \( (x-2)^{2}+(y-2)^{2}=4 \)2 answers -
2 answers
-
2 answers
-
Question 7 (10 points). Find \( y^{\prime} \) and \( y^{\prime \prime} \) a) \( y=\ln \left(x+\sqrt{1+x^{2}}\right) \) b) \( y=\ln (\sec x+\tan x) \) c) \( y=\frac{\ln x}{x^{2}} \) d) \( y=e^{\ln \lef2 answers -
Find 2 0 f (x, y) dx and 3 0 f (x, y) dy. f (x, y) = 5x + 3x2y2 2 0 f (x, y) dx= 3 0 f (x, y) dy=
Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) \[ \begin{array}{l} f(x, y)=5 x+3 x^{2} y^{2} \\ \int_{0}^{2} f(x, y) d x= \\ \int_{0}^{3} f(x, y) d y= \end{array} \]4 answers -
Find 2 0 f (x, y) dx and 3 0 f (x, y) dy. f (x, y) = 11y x + 2 2 0 f (x, y) dx= 3 0 f (x, y) dy=
Find \( \int_{0}^{2} f(x, y) d x \) and \( \int_{0}^{3} f(x, y) d y \) \[ f(x, y)=5 x+3 x^{2} y^{2} \] \( \int_{0}^{2} f(x, y) d x= \) \( \int_{0}^{3} f(x, y) d y= \)2 answers -
Find the Jacobian of the transformation. \[ x=-6 u+5 v, y=-6 u+-6 v \] \[ \frac{\partial(x, y)}{\partial(u, v)}= \]2 answers -
Find the Jacobian of the transformation. \[ x=-5 u^{2} v^{4}, y=u^{3} / v^{5} \] \[ \frac{\partial(x, y)}{\partial(u, v)}= \]2 answers -
Find the integral. \[ \begin{array}{l} \int \tan x \sec ^{4} x d x \\ \frac{\tan ^{2} x}{2}-\frac{\tan ^{4} x}{4}+C \\ \frac{\tan ^{2} x}{2}+\frac{\tan ^{4} x}{4}+C \\ \frac{\tan ^{2} x}{2}+C \\ 1+\fr2 answers