Calculus Archive: Questions from December 20, 2022
-
\( E=\{(r, \theta, z): 0 \leq \theta \leq \pi, 0 \leq z \leq 1,9 \sqrt{z} \leq r \leq 9\} \). Compute \[ \iiint_{E} y^{2} e^{\left(x^{2}+y^{2}\right)^{3}} d v \]2 answers -
2 answers
-
2 answers
-
Solve the following second-order differential equation: A. \( y^{\prime \prime}-2 y^{\prime}-15 y=0 \) B. \( y^{\prime \prime}-y^{\prime}+y=0 \)2 answers -
1. \( \lim _{x \rightarrow 0} \frac{\tan x}{3 x}=\square \quad \lim _{x \rightarrow \infty} \frac{\cos x}{x}= \) 2. \( \lim _{x \rightarrow 0} \cos (x+\sin x)= \) 3. The horizontal asymptote of \( f(x2 answers -
2 answers
-
2 answers
-
2 answers
-
(6 points) Find the partial derivatives of the function \[ f(x, y)=x y e^{-9 y} \] \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \)2 answers -
2 answers
-
2 answers
-
Find the symmetric equation of the normal line to the surface at the given point.
Parte I: Halle las ecuaciones simétricas de la recta normal a la superficie en el punto dado 1. \( x^{2}+y^{2}+z^{2}=9,(3,3,3) \) 2. \( z=x^{2}-y^{2},(3,2,5) \) 3. \( x y z=10,(1,25) \) 4. \( x y-z=02 answers -
2 answers
-
(6 points) Find the partial derivatives of the function \[ f(x, y)=x y e^{1 y} \] \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) \( f_{x y}(x, y)= \) \( f_{y x}(x, y)= \)2 answers -
(d) Let \( \mathbf{F}(x, y, z)=x \mathbf{i}+y \mathbf{j}+z \mathbf{k} \) and let \( f(x, y, z)=|\mathbf{F}(x, y, z)| \). Show that: i. \( \nabla \times \mathbf{F}=\mathbf{0} \). ii. \( \nabla f=\mathb2 answers -
please answer the whole question
1. \( \lim _{(x, y) \rightarrow(1,1)} \frac{x y}{x^{2}+y^{2}} \) 2. \( \lim _{(x, y) \rightarrow(0,0)} \frac{x^{2}}{\left(x^{2}+1\right)\left(y^{2}+1\right)} \) 3. \( \lim _{(x, y) \rightarrow(1,1)} \2 answers -
(15 points) Calculate \( \iint_{\mathcal{S}} f(x, y, z) d S \) For \[ \begin{array}{l} y=6-z^{2}, \quad 0 \leq x, z \leq 7 ; \quad f(x, y, z)=z \\ \iint_{\mathcal{S}} f(x, y, z) d S= \end{array} \]2 answers -
Calculate \( \int_{S} f(x, y, z) d S \) For \[ \int_{S} f(x, y, z) d S= \] \[ y=9-z^{2}, \quad 0 \leq x, z \leq 7 ; \quad f(x, y, z)=z \]2 answers -
derivative exercises
\[ x^{3}+2 x^{2} y-2 y^{2}=-5 ; P(-1,-1) \] Pág. 99, Sección III, ejercicio \# \[ x^{3} y^{2}+x^{2} y^{3}+x y=14 y ; P(2,1) \]2 answers -
2 answers
-
2 answers
-
Find \( d y / d x \) by implicit differentiation. \[ \begin{array}{r} 9 x^{2} y+3 y^{2} x=-5 \\ d y / d x=-\frac{x(3 x-2 y)}{y(6 x+y)} \end{array} \]2 answers -
2 answers