Calculus Archive: Questions from November 16, 2022
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11) The differential Equation \( y^{\prime \prime}+4 y^{\prime}+7 y=0 \) has general solution (a) \( y=e^{-2 x}\left(c_{1} \cos \ln x+c_{2} \sin \ln x\right) \) (b) \( y=x^{-2}\left(c_{1} \cos 3 x+c_{2 answers -
3. Determine the maximum height and horizontal displacement of a projectile that is fired at a height of 1.5 meters above ground level with an initial velocity of 100 meters per
3. Determine la altura máxima y el desplazamiento horizontal de un proyectil que es disparado a una altura de \( 1.5 \) metros sobre el nivel del suelo con una velocidad inicial de 100 metros por seg2 answers -
Evaluate \( \iiint_{\mathcal{B}} f(x, y, z) d V \) for the specified function \( f \) and \( \mathcal{B} \) : \[ f(x, y, z)=\frac{z}{x} \quad 3 \leq x \leq 24,0 \leq y \leq 2,0 \leq z \leq 10 \] \[ \i2 answers -
Differentiate. \[ y=\frac{\sqrt{x}}{2 x}-3 \] a. \[ y^{\prime}=\frac{-1}{x \sqrt{x}} \] \( y^{\prime}=\frac{-1}{4 x \sqrt{x}} \) c. \( y^{\prime}=\frac{1}{4 x \sqrt{x}} \) d. \[ y^{\prime}=\frac{1}{x2 answers -
Find \( d y / d x \) for each of the following: a. \( y=8 x^{4}+2 \sqrt{x} \) b. \( f(x)=x^{-1}\left(x^{2}+1\right) \sqrt{x} \) c. \( y=\frac{3 x-1}{x^{2}+x+1} \) d. \( y=5\left(1+x^{2}\right)^{4} \)2 answers -
find the dy/dx for each following
e. \( y=\left(1+\frac{1}{x}\right)-\left(1+\frac{1}{x}\right)^{6} \) f. \( f(x)=x^{3} e^{x} \) g. \( y=5 e^{2 x^{2}-3 x+1} \) h. \( f(x)=\ln x+3 x-2 \) i. \( y=e^{x} \ln x \) j. \( \quad y=e^{x^{3}} \1 answer -
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Find the derivative of the function. 6) \( h(x)=\left(\frac{\cos x}{1+\sin x}\right)^{6} \) A) \( \frac{-6 \cos ^{5} x}{(1+\sin x)^{6}} \) B) \( -6\left(\frac{\sin x}{\cos x}\right)^{5} \) C) \( 6\lef2 answers -
Multiplique los siguientes números complejos. \( 50 \angle 10^{\circ} \) por \( 30 \angle-40^{\circ} \) \( 42 \angle 20^{\circ} \) por \( 20 \angle-10^{\circ} \).2 answers -
(iii) Evaluate the integral \( \iint_{D}\left(3 x^{2}+y^{2}\right) d A \) where \( =\left\{(x, y) \mid-2 \leq y \leq 3, y^{2}-3 \leq x \leq y+3\right\} \). Solution:2 answers -
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termine the growth constant \( k \), then find all solutions of the differential equation. 8) \( y^{\prime}-5 y=0 \) A) \( k=5, y=5 e^{t} \) B) \( k=5, y=c e^{5 t} \) C) \( k=-5, y=C e^{-5 t} \) D) \(2 answers -
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find dy/dx for each of the followig
e. \( y=\left(1+\frac{1}{x}\right)-\left(1+\frac{1}{x}\right)^{6} \) f. \( f(x)=x^{3} e^{x} \) g. \( y=5 e^{2 x^{2}-3 x+1} \) h. \( f(x)=\ln x+3 x-2 \) i. \( y=e^{x} \ln x \) j. \( \quad y=e^{x^{3}} \2 answers -
#34 wasnt answered.
Find derivatives of the functions defined as follows. 1. \( y=e^{4 \tau} \) 2. \( y=e^{-2 x} \) 3. \( y=-8 e^{3 x} \) 4. \( y=1.2 e^{5 x} \) 5. \( y=-16 e^{2 x+1} \) 6. \( y=-4 e^{-03 x} \) 7. \( y=e^2 answers -
Can someone please help me evaluate it in a Calculus 3 way. I am very confused on these problems. Please and thank you!
Consider the integral \[ \int_{0}^{6} \int_{0}^{3-x / 2} \int_{0}^{2-x / 3-2 y / 3} f(x, y, z) d z d y d x \] Write this integral in the order \( d y d x d z \). \[ \int_{0}^{2} \int_{0}^{3 z-6} \int_2 answers -
Find \( g^{\prime}(w) \). \[ g(w)=-5 \ln \left(5+3 w+w^{4}\right) \] \[ g^{\prime}(w)= \] SCALCET7 3.6.507.XP. Differentiate the function. \[ y=\left(\ln \left(1+e^{x}\right)\right)^{9} \]2 answers -
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Consider a particle that moves with a trajectory given by: r(t)= x(t)i+y(t)j+z(t)k Discuss any change in position, velocity, and acceleration of the particle if its position is given by vector functi
Considerar una particula que se mueve con una trayectoria dada por: \[ r(t)=x(t) i+y(t) j+z(t) k \] Discuta todo cambio en posición, velocidad y aceleración de la particula si su posición está dad2 answers -
1. Find r(t) for the following condition r' (t) = 4e^2tj + 3e^etj , r(0) = 2i 2. Find r"(t) of the following function r(t) = 4 costi + 4 sin t j 3. Determin the maximum height and horizontal displac
1. Halle \( r(t) \) para la siguiente condición \( r^{\prime}(t)=4 e^{2 t} i+3 e^{t} j, r(0)=2 i \) 2. Halle \( r^{\prime \prime}(t) \) de la siguiente función \( r(t)=4 \cos t i+4 \sin t j \) 3. De1 answer -
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Compute the gradient vector fields of the following functions: \[ \begin{array}{ll} \text { A. } f(x, y)=9 x^{2}+9 y^{2} & \\ \nabla f(x, y)= & \text { I+ } \end{array} \] B. \( f(x, y)=x^{3} y^{9} \)2 answers -
Evaluate the double integral. \[ \iint_{D} \frac{4 y}{2 x^{5}+1} d A, \quad D=\left\{(x, y) \mid 0 \leq x \leq 1,0 \leq y \leq x^{2}\right\} \]2 answers -
Solve the initial value problem \[ \mathbf{y}^{\prime}=\left(\begin{array}{cc} 2 & 0 \\ 1 & -1 \end{array}\right) \mathbf{y}, \quad \mathbf{y}(0)=\left(\begin{array}{c} 1 \\ -1 \end{array}\right) \]2 answers -
termine the growth constant \( k \), then find all solutions of the differential equation. 8) \( y^{\prime}-5 y=0 \) A) \( k=5, y=5 e^{t} \) B) \( k=5, y=c e^{5 t} \) C) \( k=-5, y=C e^{-5 t} \) D) \(2 answers -
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1. Find the derivative, \( y^{\prime} \), of the following expressions, you need not simplify the resulting derivative. (a) \( y=\sqrt{x}(x-\cos x)^{3} \) (b) \( y=\frac{e^{2 x}}{1-e^{2 x}} \) (c) \(1 answer -
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just 204 please:)
In the following exercises, evaluate the triple integrals over the bounded region \[ E=\left\{(x, y, z) \mid g_{1}(y) \leq x \leq g_{2}(y), c \leq y \leq d, u_{1}(x, y) \leq z \leq u_{2}(x, y)\right\}3 answers -
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\( \begin{aligned} \text { find } c_{1} e C_{2}+y^{\prime \prime}-4 y^{\prime}+5 y=16 \cos x, & y(0)=0, y^{\prime}(0)=0, & y_{c}=c_{1} e^{2 x} \cos x+c_{2} e^{2 x} \sin x \\ & & y_{p}=2 \cos x-2 \sin2 answers -
El diagrama muestra un poligono tormado por rectángulos: ¿Cust ese fierimetro, en ples, del poligono? 105 185 [4] 4. D. 2102 answers -
hello I need help in question #7
1-8 Find (a) the curl and (b) the divergence of the vector field. 1. \( \mathbf{F}(x, y, z)=x y^{2} z^{2} \mathbf{i}+x^{2} y z^{2} \mathbf{j}+x^{2} y^{2} z \mathbf{k} \) 2. \( \mathbf{F}(x, y, z)=x^{32 answers