Calculus Archive: Questions from June 30, 2023
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Solve the simultaneous equations. a) \[ \begin{array}{l} \frac{3 y}{2}-\frac{5 x}{3}=-2 \\ \frac{y}{3}+\frac{x}{3}=\frac{13}{6} \end{array} \] b) \[ \begin{array}{l} x-y=3 \\ \frac{x}{3}+\frac{y}{2}=62 answers -
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For the function, find the partials \( f_{x}(x, y) \) and \( f_{y}(x, y) \). \[ f(x, y)=\ln \left(x^{4}+y^{7}\right) \] (a) \( f_{x}(x, y) \) (b) \( f_{y}(x, y) \)2 answers -
1) f (-2csc² x) dx = a) - 2) S a) b) c) 2 b) c) 2 cotx + C 2 d) 3 -csc³ x + C 3 2 4 csc² x cotx + C -csc ³ x + C 9 1 √2x+1 1 dx +C 2 √x² + x √2x+1+C 1/2 √2x+1+C 2 d) √√x² + x +C =
1) \( \int\left(-2 \csc ^{2} x\right) d x= \) a) \( -\frac{2}{3} \csc ^{3} x+C \) b) \( -4 \csc ^{2} x \cot x+C \) c) \( 2 \cot x+C \) d) \( -\frac{2}{9} \csc ^{3} x+C \) 2) \( \int \frac{1}{\sqrt{2 x2 answers -
necesito ayuda con la pregunta 3,4 y 5
3) \( \int x^{2}\left(x^{3}+5\right)^{6} d x= \) a) \( \frac{1}{21}\left(x^{3}+5\right)^{7}+C \) b) \( \frac{1}{7}\left(x^{3}+5\right)^{7}+C \) c) \( \frac{x^{3}\left(x^{3}+5\right)^{7}}{21}+C \) d) \2 answers -
necesito ayuda con la pregunta 6 y 7
6) \( \int \tan ^{3} x \sec ^{2} x d x= \) a) \( \frac{1}{3} \sec ^{3} x+C \) b) \( \tan ^{3}\left(\frac{1}{2} x^{2}\right)+C \) c) \( \frac{1}{4} \tan ^{4} x+C \) d) \( 6 \tan ^{2} \sec x+C \) 7) \(2 answers -
necesito ayuda con la pregunta 9 y 10
9) \( \int\left(-2 \csc ^{2} e^{x}\right) e^{x} d x= \) a) \( -\frac{2}{3} \csc ^{3} e^{x}+C \) b) \( -4 \csc ^{2} e^{x} \cot e^{x}+C \) c) \( 2 \cot e^{x}+C \) d) \( -\frac{2}{9} \csc ^{3} e^{x}+C \)2 answers -
necesito ayuda contestando la pregunta 11, 12 y 13
11) \( \int 3 x^{2} e^{x^{3}} d x= \) a) \( e^{x^{3}}+C \) b) \( x^{3} e^{x^{3}+1}+C \) c) \( x^{2}+e^{x^{2}}+C \) d) \( \frac{1}{3} e^{x^{3}}+C \) 12) \( \int \cos 5 x d x= \) a) \( -\sin \left(\frac2 answers -
necesito ayuda contestando 14 y 15
14) \( \int\left(\frac{1+\frac{1}{x}}{x+\ln x}\right) d x= \) a) \( -\frac{1}{2}(x+\ln x)^{-2}+C \) b) \( \ln |x+\ln x|+C \) c) \( \ln |x|+\ln 1+C \) d) \( \ln |x|+\ln \frac{1}{x}+C \) 15) \( \int \fr2 answers -
16) S b) sin 1 a) sec 2 17) ex dx 2x ex √e²x - 4 a) b) -1 1 -1 c) tan 2 c) alexl -1 2 dx 2 d) ninguna de las anteriores. ex 2ex 4+e2x 2 2ex 1+e²x + C + C + C [2 tan-¹ ex] = = 2ex √1+e²x d) nin
16) \( \int \frac{e^{x} d x}{e^{x} \sqrt{e^{2 x}-4}}= \) a) \( \frac{1}{2} \sec ^{-1} \frac{\left|e^{x}\right|}{2}+c \) b) \( \sin ^{-1} \frac{e^{x}}{2}+c \) c) \( \frac{1}{2} \tan ^{-1} \frac{e^{x}}{0 answers -
necesito ayuda contestando las preguntas 18,19 y 20
18) \( \int \sec ^{3} x \sec x \tan x d x= \) a) \( \frac{1}{4} \sec ^{4} x \tan x+C \). b) \( \frac{1}{4} \tan ^{4} x \sec x+C \). c) \( \frac{1}{4} \sec ^{4} x+C \). d) ninguna de las anteriores. 192 answers -
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I need help with numbers : 17, 19, 21, 23, and 25
1-22 Differentiate. 1. \( f(x)=3 \sin x-2 \cos x \) 2. \( f(x)=\tan x-4 \sin x \) 3. \( y=x^{2}+\cot x \) 4. \( y=2 \sec x-\csc x \) 5. \( h(\theta)=\theta^{2} \sin \theta \) 6. \( g(x)=3 x+x^{2} \cos3 answers -
If \( z=f(x, y) \), where \( f \) is differentiable, and \[ \begin{array}{rlrl} x & =g(t) & y & =h(t) \\ g(5) & =5 & h(5) & =-1 \\ g^{\prime}(5) & =4 & h^{\prime}(5) & =-3 \\ f_{x}(5,-1) & =4 & f_{y}(2 answers -
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3.Maximize and Minimize \( y=5 x+y \) \[ \left\{\begin{array}{c} y+x \leq 6 \\ y \leq 2 x \\ y \geq \frac{1}{2} x \\ y+x \geq 3 \end{array}\right. \]2 answers -
solve all 3 pls
II. Evalúe los integrales. a) \( \int\left(2 x^{3}-5 x\right)^{2} d x \) b) \( \int \sec (x)\left(\frac{\operatorname{sen}(x)-1}{\cos (x)}\right) d x \) c) \( \int \frac{1}{(4 x)^{2}} d x \)2 answers -
Solve the given Differential Equation: y"+y'+1/4y=e^x * (sin(3x) - cos(3x))
Solve the given Differential Equation: \( \quad y^{\prime \prime}+y^{\prime}+\frac{1}{4} y=e^{x}(\sin (3 x)-\cos (3 x)) \)2 answers -
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Escribe el límite que representa f'(2) si f(x)=2x^2+3. La respuesta debe estar en forma de ecuación.1 answer