Calculus Archive: Questions from August 10, 2022
-
1. Which of the following DEs are linear? (a) \( t^{2} y^{\prime \prime}+t y^{\prime}+y=\sin (t) \) (b) \( y^{\prime \prime \prime}+3 y^{\prime \prime}+y^{\prime}+y=1 \) (c) \( y^{\prime \prime}+\sin3 answers -
?
Evaluate: \( \iint 6 x^{5} e^{x^{3} y} d R \) where \( R=\{(x, y): 0 \leq x \leq 2,0 \leq y \leq 2\} \)1 answer -
?
Evaluate: \( \iint \sqrt{\frac{x}{y}} d A \) where \( R=\{(x, y): 0 \leq x \leq 1,1 \leq y \leq 4\} \)1 answer -
16. Given: \( \int_{1}^{8} f(x) d x=10 ; \int_{2}^{4} f(x) d x=3 ; \int_{4}^{8} f(x) d x=4 \). Find \( \int_{2}^{1} f(x) d x=? \)1 answer -
(1) \( \left(10\right. \) pts.) Let \( x=u w+v, y=w-u-v \) and \( z=v^{2} \). Find the Jacobian, \( \frac{\partial(x, y, z)}{\partial(u, v, w)} \).1 answer -
Match each function with its contour plot. \[ \begin{array}{l} f(x, y)=\sin (x-y) \\ f(x, y)=\sin \sqrt{x^{2}+y^{2}} \\ f(x, y)=\sin (x+y) \\ f(x, y)=\cos x \\ f(x, y)=\sin x \\ f(x, y)=\cos \sqrt{x^{3 answers -
Ejercicio 3: Evalúe la integral \[ \iint_{R} \frac{x y^{2}}{x^{2}+1} d A \] Donde \( R=\{(x, y) \mid 0 \leq x \leq 1,-3 \leq y \leq 3\} \)1 answer -
solve: 1.find the area enclosed by the ellipse. 2.find the area of the region under the given curve.
1. Determine el área encerrada por la elipse \( \frac{x^{2}}{25}+\frac{y^{2}}{4}=1 \) 2. Determine el área de la región bajo la curva dada \( y=\frac{1}{x^{2}+x}, 1 \leq x \leq 2 \)3 answers -
Determine el área encerrada por la elipse \( \frac{x^{2}}{25}+\frac{y^{2}}{4}=1 \) Determine el área de la región bajo la curva dada \( y=\frac{1}{x^{3}+x}, 1 \leq x \leq 2 \)1 answer -
Suppose: \( f(2)=2 \) \( f^{\prime}(2)=3 \) \( g(2)=1 \) \( g^{\prime}(2)=5 \) Find \( j^{\prime}(2) \) if \( j(x)=\frac{f(x)}{g(x)} \)1 answer -
1 answer
-
Solve the following integrals, using the most appropriate technique, integration by parts or tabulation
Ejercicios de práctica: Resuelve las siguientes integrales, utilizando la técnica más apropiada, integración por partes o tabulación. 1. \( \int x^{3} \ln x d x \) 2. \( \int \cos ^{-1} x d x \)1 answer -
1 answer
-
Evaluate the integral. \[ \int 9 \cos ^{3} 3 \theta \sin 3 \theta d \theta \] \[ \int 9 \cos ^{3} 3 \theta \sin 3 \theta d \theta= \]1 answer -
1 answer
-
6. Parameterize the following curve 25x2−250x+ 49y2−98y+ 674 = 1225. 7.SeaT:P2(x)→P2(x)\T(ax2+bx+c) = (a+b−2c)x2+ (2a+ 11c−9b)x+ (3a−8b+ 9c). DetermineKer(T) 8.8. Let B={3x2+ 10.5x2+ 11x,7
ancha con lipix, pierde d deredio a reclames. Ws ma prueba de desurro lo, por lo que deberin apareser tadox los pasas que wiliah parn oblener h ofpurath correcth 1. Determine si \( A=\left\{(x, y, z)1 answer -
( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}+4 y^{\prime}=0, \] \[ y(0)=-4, y^{\prime}(0)=6, y^{\prime \prime}(0)=12 \]1 answer -
(1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-15 y^{\prime \prime}+56 y^{\prime}=168 e^{x}, \] \[ y(0)=29, y^{\prime}(0)=25, \quad y^{\prime \prime}(0)=22 \] \[ y(x)=1 answer -
3 answers
-
(1 point) Solve the initial value problem \[ y^{\prime \prime}+1 x y^{\prime}-4 y=0, y(0)=6, y^{\prime}(0)=0 \]1 answer -
3 answers