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Calculus Archive: Questions from September 25, 2022

• solve this orde n diferential equation please
  5. \( \quad \frac{d^{3} y}{d x^{3}}-2 \frac{d^{2} y}{d x^{2}}-\frac{d y}{d x}+2 y=9 e^{2 x}-8 e^{3 x} \) 6. \( \quad \frac{d^{3} y}{d x^{3}}-4 \frac{d^{2} y}{d x^{2}}+5 \frac{d y}{d x}-2 y=3 x^{2} e^{
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  \( y^{\prime}-y=f(t) \) where \( f(t)=\left\{\begin{array}{cc}0 & 0 \leq t3\end{array}, y(0)=0\right. \)
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  Find \( \lim _{x \rightarrow \infty} f(x) \) if, for all \( x>1 \) \[ \frac{16 e^{x}-22}{4 e^{x}}
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  3 Determine if there is a unique solution (1). \( (10 \%) y^{\prime}=\sqrt{y}, y(0)=1 \) (2). \( (10 \%) y^{\prime}=-\sqrt{1-y^{2}}, y(0)=0 \) \( (3) \cdot(10 \%) y^{\prime}=-\sqrt{1-y^{2}}, y(0)=1 \)
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• Translation: Demonstrate the convergence or divergence of the series, using the criterion of reason ( equation) a. Converges by reason criterion b. Diverges by reason c. The criterion of reasonablenes
  1. Demuestre la convergencia o divergencia de la serie, utilizando el criterio de la razón \( \quad \sum_{n=1}^{\infty} \frac{n !}{(n-4) !} \) a. Converge por el criterio de la razón b. Diverge por
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• Translation: 2. Demonstrate the convergence or divergence of the series, using the root criterion ( equation) a. Converges by root criterion b. Diverges by root criterion c. The criterion of reasonabl
  2. Demuestre la convergencia o divergencia, utilizando el criterio de la raíz. \[ \sum_{n=1}^{\infty} \frac{n^{7}}{7^{n}} \] a. Converge por el criterio de la raiz b. Diverge por el criterio de la ra
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• Translation: 3. Demonstrate convergence and divergence of ( equation) a. Diverges b. Conditionally converges c. It converges absolutely d. No convergence or divergence
  3. Demuestre la convergencia y divergencia de \( \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} \) a. Diverge b. Converge Condicionalmente c. Converge absolutamente d. No se puede mostrar convergencia o div
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• Maximize: f(x, y) = x2 + y2 , x, y > 0 subject to the constraint x3 + y3 = 16.
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  Match each graph with its equation. \[ \begin{aligned} f(x, y) &=x^{2}+y \\ f(x, y) &=\sqrt{x^{2}+2 \cdot y^{2}} \end{aligned} \] \( f(x, y)=x^{3} \) \( f(x, y)=y^{2} \) \[ f(x, y)=\frac{1}{1+x^{2}+y^
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  \[ \begin{array}{l} y=\frac{(x+5)(x+2)}{(x-5)(x-2)} \\ y^{\prime}=\frac{-x^{2}+20}{(x-5)^{2}(x-2)^{2}} \\ y^{\prime}=\frac{14 x^{2}-140}{(x-5)^{2}(x-2)^{2}} \\ y^{\prime}=\frac{14 x-140}{(x-5)^{2}(x-2
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  1. Differentiate the function. (a) \( f(x)=e^{5} \) (b) \( f(x)=\left(3 x^{2}-5 x\right) e^{x} \) (c) \( y=\frac{e^{x}}{1-e^{x}} \) (d) \( g(x)=e^{x^{2}-x} \) (e) \( y=e^{\tan \theta} \) (f) \( y=x^{2
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  (1 point) Utiliza el método de Newton-Raphson para encontrar la abscisa del punto de intersección de las gráficas de las funciones \( g(x)=e^{7 x} \) y \( f(x)=7 x \). Inicia las iteraciones en \(
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  Differentiate the function. \[ y=\log _{2}(\sec (x)) \]
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  If \( f(x, y)=\frac{x^{2} y}{\left(5 x-y^{2}\right)} \), find the following (a) \( f(1,3) \) (b) \( f(-5,-1) \) (c) \( f(x+h, y) \) (d) \( f(x, x) \)
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• I. Use the double integral to check that the moments of inertia in the region about the axes are as illustrated in the figure. Then calculate the radius of gyration about each axis: II. Determine the
  I. Utilice la integral doble para comprobar que los momentos de inercia en la región con respecto a los ejes son los que se ilustran en la figura. Luego calcule los radios de giro con respecto a cada
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  Problem 1 Find all solutions of the equation. - \( y^{\prime}=\frac{4 x y}{x^{2}+1} \) - \( t(y-1) d t+y(t+1) d y=0 \) - \( x^{2} y y^{\prime}-e^{y}=0 \) \( \sin x d x-2 y d y=0 \) - \( y^{\prime}=\fr
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  Evaluate the integral. \[ \int \frac{\sqrt{y^{2}-25}}{y} d y, y>5 \] \[ \int \frac{\sqrt{y^{2}-25}}{y} d y= \]
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  Find \( y^{\prime} \) and \( y^{\prime \prime} \). \[ y=e^{6 e^{x}} \]
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• Determine which of the following series converge?
  Determinar cuál de las siguientes series converge. \( \sum_{n=1}^{\infty}\left(4+(-1)^{n}\right)^{n} \) \( \sum_{n=0}^{\infty} 5\left(\frac{3}{2}\right)^{n} \) \( \sum_{n=1}^{\infty} \frac{1}{\sqrt{n
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  Differentiate the function. \[ y=\frac{9 x^{2}-8}{3 x^{3}+4} \]
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  Find the derivative of the function. \[ \begin{array}{l} y=\frac{(x+5)(x+2)}{(x-5)(x-2)} \\ y^{\prime}=\frac{-14 x^{2}+140}{(x-5)^{2}(x-2)^{2}} \\ y^{\prime}=\frac{14 x^{2}-140}{(x-5)^{2}(x-2)^{2}} \\
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  Find \( d y / d x \) by implicit differentiation. \[ y \sin \left(x^{2}\right)=-x \sin \left(y^{2}\right) \] \[ d y / d x= \]
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  Find the partial derivatives of the function \[ f(x, y)=x y e^{-5 y} \] \[ \begin{array}{l} f_{x}(x, y) \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \end{array} \]
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  Utilice coordenadas polares para escribir y evaluar la integral doble \( \int_{R} \int_{R} f(x, y) d A \) Para \( f(x, y)=x+y \) donde \( R: x^{2}+y^{2} \leq 4, x \geq 0, y \geq 0 \)
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  a. \( \lim _{x \rightarrow 3} \frac{e^{-x+2}-e^{-1}}{x-3} \) \( f(x)= \) b. \( \lim _{h \rightarrow 0} \frac{\cos (h+\pi)+1}{h} \); \( f(\theta)= \) \( \lim _{y \rightarrow 1 / 3} \frac{\frac{1}{y}-3}
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  Find the first partial derivatives of the function. \[ f(x, y)=\frac{x}{y} \] \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]
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  Differentiate. \[ y=\frac{2 x}{5-\tan (x)} \] \[ y^{\prime}= \]
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  Differentiate the function. \[ y=\frac{9 x^{2}-2}{7 x^{3}+5} \] \[ y^{\prime}= \]
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  If \( f(x, y)=\frac{x^{2} y}{\left(3 x-y^{2}\right)} \), find the following. (a) \( f(1,5) \) (b) \( f(-3,-1) \) (c) \( f(x+h, y) \) (d) \( f(x, x) \)
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• Find y`
  \( y=\left[\int_{0}^{x}\left(t^{3}+1\right)^{10}\right] \)
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  Find \( d y / d x \) by implicit differentiation. \[ 7 \cos x \sin y=1 \] \[ y^{\prime}= \]
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  \( g(x, y, z)=\ln \left(7 x^{2}+5 y^{3}+3 z^{4}\right) \)
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  \( \int_{|z|=3} \frac{(3 z+2)^{2}}{z(z-1)(2 z+5)} d z \)
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