Calculus Archive: Questions from September 18, 2023
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17. Given the graph of the function \( y=f(x) \), sketch the graph of each function. a) \( y=2 \sqrt{f(x)}-3 \) b) \( y=-\sqrt{2 f(x-3)} \) c) \( y=\sqrt{-f(2 x)+3} \) d) \( y=\sqrt{2 f(-x)-3} \)1 answer -
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1. Sketch the following(if possible): (a) \( y=3.4^{x} \) (b) \( y=-3.4^{x} \) (c) \( y=-3 \cdot 4^{x} \) 2. Solve the following: (a) \( 16=2^{2 x-3} \) (b) \( 625^{2 x}=125^{x+4} \)1 answer -
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\( \begin{array}{l}\int \frac{x^{3}-5 x^{2}+x-1}{x^{2} \sqrt{x}} d x \\ \int(5 \sin 2 \theta-7 \cos (4-5 \theta)) d \theta \\ \int \sec \theta(\sin \theta \tan \theta+\cos \theta) d \theta \\ \int \fr1 answer -
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\[ \begin{array}{l} \text { Given } f(x, y)=-2 x^{5}+3 x y^{2}-6 y^{3} \text {, } \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \end{array} \] Question Help: \( \square \) Video \( \square \) Post to forur1 answer -
Find the general solution of 1. \( y^{\prime \prime}-2 y^{\prime}+5 y=0 \) 2. \( 4 y^{\prime \prime}-4 y^{\prime}+y=0 \) 3. \( x^{2} y^{\prime \prime}-6 x y^{\prime}+12 y=0 \) 4. \( x^{2} y^{\prime \p1 answer -
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12. ¿ Cual de las siguientes funciones es continua en todos los números reales? a. \( y=P(x) \) donde \( P \) es un polinomio. b. \( y=\sin x \) c. \( y=\frac{1}{x^{2}+1} \) d. Todas las anteriores.1 answer -
Find and sketch the domain of the function. \[ f(x, y, z)=\ln \left(81-9 x^{2}-9 y^{2}-z^{2}\right) \]1 answer -
If the series is conditionally convergent, determine which of the following series is divergent.
¿ı la serıe \( \sum_{n=1}^{\infty} a_{n} \) es condıcıonalmente convergente, determıne cuál de las sıguientes serıes es divergente. \[ \begin{array}{l} \sum_{n=1}^{\infty}\left(a_{n}\right)^{1 answer -
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 \( y=\frac{1}{x^{2}+x}, 1 \leq x \leq 2 \)1 answer -
Evalúe las siguientes integrales: 1. \( \int \frac{d x}{x^{2} \sqrt{9-x^{2}}} \) 2. \( \int \frac{\sqrt{x^{2}-3}}{x} d x \) 3. \( \int_{0}^{3} \frac{x^{3}}{\sqrt{x^{2}+9}} d x \) 4. \( \int \frac{d x1 answer -
Find all the vertical asymptotes the function \( f(x)=\frac{3 x^{2}-6}{x^{2}-2 x} \) using limits, if possible.1 answer -
Use la regla de la cadena para encontrar \( \frac{\partial w}{\partial s} \) si \( w=x y^{2}+x z^{2} . x=t+1, y=t-1, z=s t \) cuando \( =2 \) y \( t=1 \). (Muestre su trabajo para recibir puntuación)0 answers -
Evaluate the integral. cos y dy S 2. sin y+sin y - 12
Evaluate the integral. \[ \int \frac{\cos y d y}{\sin ^{2} y+\sin y-12} \]1 answer -
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Differentiate. y' = y = t (t - 3)² Differentiate y=x4/1-x3
Differentiate. \[ y=\frac{t}{(t-3)^{2}} \] \[ y^{\prime}= \] Differentiate. \[ \begin{array}{c} y=\frac{x^{4}}{1-x^{3}} \\ \frac{-x+4 x^{3}}{\left(-x^{3}+1\right)} \\ y^{\prime}=\frac{1}{1} \end{arra1 answer -
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6. La siguiente función f NO es continua en x = 0: a. f(x) = tan x b. f(z)=sinx cot x c. f(x) = sec x d. niguna de las anteriores
6. La siguiente función \( f \) NO es continua en \( x=0 \) : a. \( f(x)=\tan x \) b. \( f(x)=\sin x \cot x \) c. \( f(x)=\sec x \) d. niguna de las anteriores1 answer -
vectorial
(20 Pts.) El movimiento de una partícula en el espacio tridimensional se describe mediante la función vectorial \[ r(t)=b \cos t i+b \sin t \boldsymbol{j}+c t \boldsymbol{k} \quad t \geq 0 \] a) Cal1 answer -
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(20 Pts.) El movimiento de una partícula en el espacio tridimensional se describe mediante la función vectorial \[ r(t)=b \cos t i+b \sin t \boldsymbol{j}+c t \boldsymbol{k} \quad t \geq 0 \] a) Cal1 answer -
3. Solve the initial value problem: \[ y^{\prime}-y \tan x=x \sec x, y(0)=1 \text { with } x \in[0, \pi / 2) . \]1 answer -
6. \( (20 \) pts.) Dada la integral \[ \iint_{R} \frac{y}{x^{2}+y^{2}} d A, \] acotada por el trapezoide \( R: y=x, y=2 x, x=1, x=2 \). Utilice el orden más conveniente para evaluar la integral sobre1 answer -
Please help me
Si la serie \( \sum_{n=1}^{\infty} a_{n} \) es condicionalmente convergente, determine cuál de las siguientes series es divergente \[ \begin{array}{l} \sum_{n=1}^{\infty}(a)^{2} \\ \sum_{n=1}^{\infty1 answer -
Determine el límite \( \lim _{(x, y) \rightarrow(0,0)} f(x) \) donde la función \( f \) está definida por \[ f(x, y)=\left\{\begin{array}{cc} \frac{x^{2}-y^{4}}{x^{2}+y^{2}}, & (x, y) \neq(0,0) \\1 answer -
Calculate all Four second-order partial derivatives of \( f(x, y)=3 x^{2} y+5 x y^{3} \). \[ \begin{array}{l} F_{x x}(x, y)= \\ F_{x y}(x, y)= \\ F_{y x}(x, y)= \\ F_{y y}(x, y)= \end{array} \]1 answer -
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Find all the second partial derivatives. f(x, y) = x^y - 2x³y² fxx(x, y) = = fxy(x, y) = fyx(x, y) = fyy(x, y) = ڈے
Find all the second partial derivatives. \[ \begin{array}{l} \quad f(x, y)=x^{4} y-2 x^{3} y^{2} \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \]1 answer -
Differentiate the function. y' = y = 8ex + 3 7 VX X
Differentiate the function. \[ y=8 e^{x}+\frac{7}{\sqrt[3]{x}} \] \[ y^{\prime}= \]1 answer -
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P3) \( \mathrm{Si} \sum_{i=1}^{5} a_{i}=7 \) entonces \( \sum_{i=1}^{5}\left(3 a_{i}+4\right)= \) a) 25 b) 21 c) 31 d) 41 e) ninguna de las anteriores1 answer -
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12.5 Problem 8 Help Please help
Express the integral \( \iiint_{R} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, x=0, z=y-2 x \) and \( y=4 \). \[ \begin{arra0 answers