Calculus Archive: Questions from November 17, 2022
-
In Exercises 1-14 find a particular solution. 1. \( y^{\prime \prime}-3 y^{\prime}+2 y=e^{3 x}(1+x) \) 2. \( y^{\prime \prime}-6 y^{\prime}+5 y=e^{-3 x}(35-8 x) \) 3. \( y^{\prime \prime}-2 y^{\prime}2 answers -
2 answers
-
1. Find the derivatives of the following functions: (1) \( y=\sqrt[3]{x}(2+\sqrt{x}) \); (2) \( y=3 \mathrm{e}^{x} \cos x \); (3) \( y=a^{x}\left(x^{2}-3 x+1\right)(a>0) \); (4) \( y=\tan x \sec x \);2 answers -
(1 point) Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=x \) and \( R=[2,7] \times[2,8] \). \( \iint_{R} f(x, y) d A= \)2 answers -
What is the ODE for the solution of \( y=2 e^{x}-x-1 \) A. \( d y / d x=-x-y \) B. \( d y / d x=x+y \) C. \( d y / d x=x-y \) D. \( d y / d x=-x+y \)2 answers -
show all steps and box answer
Solve the initial value problem. \[ (x+5) \frac{d y}{d x}-2\left(x^{2}+5 x\right) y=\frac{e^{x^{2}}}{x+5}, x>-5, y(0)=5 \] Choose the correct answer below. A. \( y=\frac{24}{5} e^{x^{2}}-\frac{e^{x^{22 answers -
3. Sketch the vector field \( \mathbf{F}(x, y)=\langle 0,-y\rangle \) 4. Sketch the vector field \( \mathbf{F}(x, y)=\langle-y, x\rangle \).2 answers -
2 answers
-
tu larieo natratelt 3. Halla el lareo de la core \( y=\frac{1}{6}\left(x^{2}+4\right) \) deale \( x=0 \) hasas \( x=1 \).0 answers -
Differentiate Implicitly (4 marks each) a. \( x^{4}(x+y)=y^{2}(3 x-y) \) b. \( \tan (x-y)=\frac{y}{1+x^{2}} \)2 answers -
2) \( \lim _{x \rightarrow 1^{-}}(1-x)^{\ln x} \) II Heructive 1) \( \int_{0}^{\infty} \frac{x i x}{x^{4}+4} \) \( 24 \int_{0}^{4} \frac{d x}{x \sqrt{x^{2}}+9} \)0 answers -
tu larieo natratelt 3. Halla el lareo de la core \( y=\frac{1}{6}\left(x^{2}+4\right) \) deale \( x=0 \) hasas \( x=1 \).0 answers -
Evaluate \( \iiint_{w} f(x, y, z) d V \) for the function \( f \) and region \( W \) specified: \[ f(x, y, z)=24(x+y) \quad w: \] \[ \iiint_{w}(24(x+y)) d V= \]2 answers -
Find a particular solution to \[ y^{\prime \prime}+2 y^{\prime}+y=\frac{13.5 e^{-t}}{t^{2}+1} \] \[ y_{p}= \]2 answers -
2 answers
-
Let \( y \) be the solution of the initial value problem \[ y^{\prime \prime}+y=-\sin (2 x), y(0)=0, y^{\prime}(0)=0 \]2 answers -
2 answers
-
ejer 4 calculo 3
Evaluate the definite integrais \[ \int_{0}^{4}\left\|t \mathbf{i}+t^{2} \mathbf{j}\right\| d t \]2 answers -
2 answers
-
2 answers
-
2 answers
-
help solve
(8) Find the differential for the function using logarithmic differentiation. \( y=(\sin x)^{(\sec x)} \) : (A) \( \ln y=\sec x \cdot \ln (\sin x) \) and so \( d y=y^{\prime} d x=(\sin x)^{(\sec x)}[\2 answers -
2 answers
-
-2 Vocabulario. Elena and Pablo are churting about their university experience. Complete their conversation with the worda provided Fach ward ahaili niks her E.ENAL CY dóndevives? Jen una residencia0 answers -
\[ y^{\prime \prime}+y=\tan x \] Hint: \( \int \frac{-\sin ^{2} x}{\cos x} d x=\int \frac{\cos ^{2} x-1}{\cos x} d x=\int\left(\frac{\cos ^{2} x}{\cos x}-\frac{1}{\cos x}\right) d x=\int \cos x d x-\i2 answers -
Find all complementary functions of the equation \( y^{\prime \prime}-4 y^{\prime}+4 y=0 \). a. \( \cos 2 x, \sin 2 x \) b. \( e^{-2 x}, x e^{-2 x} \) c. \( e^{2 x}, x e^{2 x} \) d. \( e^{2 x}, e^{2 x2 answers -
5. Evaluate \( \iint_{R}(x-y) d A \) where \( R=\left\{(x, y): 4 \leq x^{2}+y^{2} \leq 16\right. \) and \( \left.y \leq x\right\} \) \( \frac{112}{3} \sqrt{2} \)2 answers -
2 answers
-
2 answers
-
2 answers
-
In the following exercises, evaluate the triple integrals \( \iiint_{E} f(x, y, z) d V \) over the solid \( E \). \[ \text { 241. } f(x, y, z)=z, B=\left\{(x, y, z) \mid x^{2}+y^{2} \leq 9, x \geq 0,2 answers -
2 answers
-
18. \( f(x, y)=\sin x+\sin y+\cos (x+y) \), \( 0 \leqslant x \leqslant \pi / 4,0 \leqslant y \leqslant \pi / 4 \) 16. \( f(s, t)=t e^{s t}, \quad(0,2) \)0 answers -
serie de una sola malla cuando \( \underline{\underline{i}(0)}=0, L=1 h, R=10 \Omega \) y \( E(t) \) es como en la figura. Use un programa de computadora para graficar y dibuje \( i(t) \) en el interv1 answer -
\( \sin ^{2} \theta+\sec ^{2} \theta-1=\frac{\left(1-\cos ^{2} \theta\right)\left(1+\cos ^{2} \theta\right)}{\cos ^{2} \theta} \)2 answers -
Determine the global extreme values of the function \( f(x, y)=2 x^{3}+2 x^{2} y+5 y^{2}, \quad x, y \geq 0, x+y \leq 1 \) \[ \begin{array}{c} f_{\min }= \\ f_{\max }= \end{array} \]2 answers -
2 answers
-
4. \( \int \frac{d y}{6 y-2-9 y^{2}} \) 5. \( \int \frac{(1+\tan x) d x}{\cos ^{2} x \sqrt{4-9 \tan ^{2} x}} \)2 answers