Calculus Archive: Questions from April 03, 2023
-
2 answers
-
7. (15 pts, \( 5 \mathrm{pts} \mathrm{c} / \mathrm{u}) \) Determine la convergencia o divergencia de cada sucesión. Si la sucesión converge, encuentre su limite. a) \( a_{n}=3+\left(\frac{2}{7}\righ2 answers -
10. (6pts) Construya una serie geométriea \( \sum \frac{13}{2} r^{n-1} \) que converja al nímero 5 . 11. ( 8 pts) Los extremos de un abrevadero de \( 2 \mathrm{ft} \) de largo thenen forma de un tra2 answers -
11. ( 8 pts) Los extremos de un abrevadero de \( 2 \mathrm{ft} \) de largo tienen forma de un trapecio isósceles cuya base inferior mide \( 1 \mathrm{ft} \), su base superior mide \( 1.5 \mathrm{ft}2 answers -
Find \( \frac{\partial f}{\partial s} \) and \( \frac{\partial f}{\partial t} \) when \( f(x, y)=e^{x} \cos y, x=2 s^{2}-t^{2} \) and \( y=3 \) st. \[ \frac{\partial f}{\partial s}= \] \[ \frac{\parti2 answers -
2 answers
-
Determine the absolute maximum and minimum
\( f(x, y)=4 x+6 y-x^{2}-y^{2} \) \( E=\{(x, y) \mid 0 \leq x \leq 4,0 \leq y \leq 5\} \)2 answers -
2 answers
-
7 Hallar una ecuación del plano tangente y ecuaciones simétricas de la línea normal a la superficie en el punto dado a. \( 3 x^{2}+\frac{1}{2} y^{2}-z=9,(1,2,4) \)2 answers -
2 answers
-
3. (4) Solve the I.V.P. \( \frac{d y}{d x}=2 x^{2} \cos ^{2}(y), y(0)=\frac{\pi}{4} \quad y^{\prime}(x)=\frac{d y}{d x} \) y at the erel2 answers -
0 answers
-
Calculate the double integral. \[ \iint_{R}\left(2 y+x y^{-2}\right) d A, \quad R=\{(x, y) \mid 0 \leq x \leq 2,1 \leq y \leq 2\} \]2 answers -
suelve \( \left(y+x \cot \frac{y}{x}\right) d x-x d y=0 \) \( \ln \cos \frac{y}{x}|=\ln | x \mid+c \) \( x \cos \frac{y}{x}=c \) \( \ln |x|=\sec ^{2}\left(\frac{y}{x}\right)+c \) Ninguna de las anteri0 answers -
2 answers
-
this is a solution of what equation?
7. \( y=\frac{x^{10}}{10}+K \) es solución de la ecuación diferencial: a) \( \frac{d y}{d x}=x^{2} \) (b) \( d y=x^{2} d x \) c) \( \frac{d y}{d x}=x y \) d) \( \frac{d y}{d x}=x+2 \)2 answers -
2 answers
-
2 answers
-
Use logarithmic differentiation to find \( y^{\prime} \). \[ y=\frac{\sqrt{4-9 x}\left(x^{2}+6\right)^{2}}{x^{2}+3 x+5} \]2 answers -
Question6
Solve the Cauchy-Euler differential equations: (5) \( x^{2} d^{2} y / d x^{2}-x d y / d x-35 y=0 \). (6) \( x^{2} d^{2} y / d x^{2}-7 x d y / d x+17 y=0 \). (7) \( x^{2} d^{2} y / d x^{2}+11 x d y / d2 answers -
Question7
Solve the Cauchy-Euler differential equations: (5) \( x^{2} d^{2} y / d x^{2}-x d y / d x-35 y=0 \). (6) \( x^{2} d^{2} y / d x^{2}-7 x d y / d x+77 y=0 \). (7) \( x^{2} d^{2} y / d x^{2}+11 x d y / d2 answers -
2 answers
-
\[ \mathbf{F}(x, y, z)=(x+y z) \mathbf{i}+(-2 y-x z) \mathbf{j}+(2 z+7 x y) \mathbf{k} \] Calculate \[ \operatorname{curl}(\mathbf{F})= \] \[ \operatorname{div}(\mathbf{F})= \]2 answers -
2 answers
-
(3) Consider the curve \( x^{5}+y^{5}=10 \). Find \( y^{\prime}, y^{\prime \prime} \). (4) Find \( y^{\prime} \) if \( \cos (x+y)=y^{2} \sin (x) \). (5) Find \( y^{\prime} \) : - \( 3 x^{2}-x+x y=2 \)2 answers -
1 answer
-
1 answer
-
2 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
Necesito ayuda para probar la derivada del producto cruzado. d/dt(A x B) = (A x dB/dt) + (dA/dt x B)0 answers
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
0 answers
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
0 answers
-
0 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
Verifique que y = sen x cos x - cos x es una solución del IVP y' + (tan x)y = cos^2x ......y(0) = -10 answers
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
1 answer
-
2 answers
-
0 answers
-
1 answer
-
1 answer