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Calculus Archive: Questions from March 21, 2023

• let u.v=i-j+2k. If possible, find u.(u.v)
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• Find the Limit !!
  \( \lim _{\substack{(x, y) \rightarrow(9,4) \\ y \neq 4}} \frac{x y+4 y-4 x-16}{y-4} \)
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  Find the limit. 2) \( \lim _{(x, y) \rightarrow(4,5)}\left(\frac{4}{x}-\frac{2}{y}\right) \) 3) \( \lim _{(x, y) \rightarrow(9,4)} \frac{x y+4 y-4 x-16}{y-4} \)
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• can anyone help me solve problem#11?
  Calculating First-order Partial Derivatives In Exercises 1-22, find \( \partial f / \partial x \) and \( \partial f / \partial y \). 1. \( f(x, y)=2 x^{2}-3 y-4 \) 2. \( f(x, y \) 3. \( f(x, y)=\left(
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• Solve the initial-value problem. y'' + 9y = 0 y (𝜋/3) = 0 y' (𝜋/3) = 4
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  \( \begin{array}{l}\frac{d}{d x}\left(\int_{\ln \left(x^{2}+1\right)}^{x^{2}} \frac{\cos (2 y)}{\sqrt[3]{y^{4}+\cos (3 y)+3}} d y\right) \\ \ln (t)=\log _{e}(t)\end{array} \)
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  \( \begin{array}{l}\text { Find } \frac{d^{2} y}{d x^{2}} \\ \qquad y=5 x+8\end{array} \) \( \frac{d^{2} y}{d x^{2}}=5 \)
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  Question 7 Find the indefinite integral. \[ \int \sin ^{3}(3 \theta) \cdot \sqrt{\cos (3 \theta)} \mathrm{d} \theta \] \[ \begin{array}{l} \frac{2}{9}(\cos (3 \theta))^{\frac{3}{2}}-\frac{2}{21}(\cos
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• 𝑓(𝑥,𝑦,𝑧)=𝑥𝑦𝑧=6 f ( x , y , z ) = x y z = 6 at point (1,2,3) ( 1 , 2 , 3 )
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• Hallar las pendiente de las recta tangente f(x)=-3x^(2)-2x+15 en el punto x=2
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  (1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-8 y^{\prime \prime}+12 y^{\prime}=5 e^{x} \] \[ y(0)=13, \quad y^{\prime}(0)=25, \quad y^{\prime \prime}(0)=29 \]
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  (1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-9 y^{\prime \prime}-y^{\prime}+9 y=0 \] \[ \begin{array}{l} y(0)--4 \quad v^{\prime}(n)--2 \quad v^{\prime \prime}(\cap)-
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  (1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-9 y^{\prime \prime}-y^{\prime}+9 y=0 \] \[ y(0)=0, \quad y^{\prime}(0)=3, \quad y^{\prime \prime}(0)=0 \text {. } \] \[ y
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• Construir. la tabla. de valories dela siguiente funcion. y=x^(-3)
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• f(x)=(1)/(3)x^(3)-x^(2)-8x+5 fonkiyonanun (-3;5) aralibonda alabilecebi en bogik degeri kagtir?
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• Dividir. (12x^(3)+3x^(2)+15x-15)-:(4x^(2)-3x) La respuesta debe incluir el cociente y el residu
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• te whether the given system of linear tion. 3y=9x-6 3y=6x-6
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• En el monomio: M(x;y)=3x^(2n-1)y^(n+5) Calcular el valor del GR_(x) siendo GRy =10
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• Alexys Ferrantelli oint (s) possible 1 point (s) possible f(x)=2x^(3)-3x^(2)-12x+9 (Q)
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• find y"
  Problem 3. (5 pts.) Find \( y^{\prime \prime} \) if \( 2 x^{\wedge} 3-3 y^{\wedge} 2=8 \)
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• Please show work
  Find \( d y / d x \) \[ y=\ln x^{6}+\log _{3} x-10 e^{x}+5^{x} \]
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• Dividir. (8x^(3)+16x^(2)+10x+11)-:(4x+6) La respuesta debe incluir el cociente y el residuo.
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  1. Hallar las derivadas parciales de: a. \( f(x, y)=y^{3}-4 x^{2} y-x \) b. \( g(x, y)=e^{2 y} \sin (x y) \) c. \( h(x, y, z)=\sin (2 x+y+4 z) \)
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  2. Evaluar las derivadas parciales de cada función en el punto dado: a. \( f(x, y)=\frac{x y}{x-y} \) en el punto \( (2,-2) \). b. \( g(x, y)=\frac{6 x y}{\sqrt{4 x^{2}+5 y^{2}}} \) en el punto \( (1
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  4. Para cada función hallar los valores de \( x \) y los de \( y \) tales que \( \frac{\partial f}{\partial x}(x, y)=0 \) y \( \frac{\partial f}{\partial y}(x, y)=0 \) a. \( f(x, y)=x^{2}+4 x y+y^{2}
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  Usando la regla de la cadena hallar \( \frac{\partial W}{\partial s} \) y \( \frac{\partial W}{\partial t} \) a. \( W=x \cos (y z), \quad x=s^{2}, \quad y=t^{2}, \quad z=s-2 t \) b. \( W=z e^{\frac{x}
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  6. Considere la función \( W=f(x, y) \), donde \( x=u-v, \quad y=v-u \). Verificar que \( \frac{\partial W}{\partial u}+\frac{\partial W}{\partial v}=0 \).
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  6. Considere la función \( W=f(x, y) \), donde \( x=u-v, \quad y=v-u \). Verificar que \( \frac{\partial W}{\partial u}+\frac{\partial W}{\partial v}=0 \).
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• Montrer que. (cos^(4)x-sin^(4)x)/(cos^(2)x-sin^(2)x)=1
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  Solve the initial value problems. a) \( y^{\prime \prime}+y^{\prime}=x \), and \( y(0)=1, y^{\prime}(0)=0 \) b) \( y^{\prime \prime}+y=8 \cos 2 x-4 \sin x, y(\pi / 2)=-1, y^{\prime}(\pi / 2)=-0 \)
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• can you answer both questions
  Complete the table. LARCALC12 2.4.003. Complete the table.
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  Evaluate the double integral. \[ \iint_{D} 4 x \sqrt{y^{2}-x^{2}} d A, D=\{(x, y) \mid 0 \leq y \leq 3,0 \leq x \leq y\} \]
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  Calculate the double integral. \[ \iint_{R} \frac{8\left(1+x^{2}\right)}{1+y^{2}} d A, R=\{(x, y) \mid 0 \leq x \leq 1,0 \leq y \leq 1\} \]
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• possible rational roots are actual roc 25x^(4)+25x^(3)+124x^(2)-x-5=0
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• 1.Determine the lenght of the arc in the given Interval. 2. Determine and interpret the curvature K of the curve at the value of the given parameter.
  I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \) II. Determ
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• Find partial derivatives
  1. Hallar las derivadas parciales de: a. \( f(x, y)=y^{3}-4 x^{2} y-x \) b. \( g(x, y)=e^{2 y} \sin (x y) \) c. \( h(x, y, z)=\sin (2 x+y+4 z) \)
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• Find partial derivatives in a point given
  2. Evaluar las derivadas parciales de cada función en el punto dado: a. \( f(x, y)=\frac{x y}{x-y} \) en el punto \( (2,-2) \). b. \( g(x, y)=\frac{6 x y}{\sqrt{4 x^{2}+5 y^{2}}} \) en el punto \( (1
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  3. Hallar \( \frac{\partial}{\partial x}\left(\frac{\partial f}{\partial x}\right)=\frac{\partial^{2} f}{\partial x^{2}}, \quad \frac{\partial}{\partial y}\left(\frac{\partial f}{\partial y}\right)=\f
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  4. Para cada función hallar los valores de \( x \) y los de \( y \) tales que \( \frac{\partial f}{\partial x}(x, y)=0 \) y \( \frac{\partial f}{\partial y}(x, y)=0 \) a. \( f(x, y)=x^{2}+4 x y+y^{2}
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• Using the chain rule, solve:
  Usando la regla de la cadena hallar \( \frac{\partial W}{\partial s} \) y \( \frac{\partial W}{\partial t} \) a. \( W=x \cos (y z), \quad x=s^{2}, \quad y=t^{2}, \quad z=s-2 t \) b. \( W=z e^{\frac{x}
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  Considere la función \( W=f(x, y) \), donde \( x=u-v, \quad y=v-u \). Verificar que \( \frac{\partial W}{\partial u}+\frac{\partial W}{\partial v}=0 \).
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  Find the differential df. \[ f(x, y)=x \cos (y)-2 y \cos (x) \] a) \( \bigcirc \) df \( =(-x \sin (y)-2 \cos (x)) \Delta x+(\cos (y)+2 y \sin (x)) \Delta y \) b) \( \mathrm{df}=(\cos (y)+2 y \sin (x))
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  Find the differential df. \[ f(x, y)=\ln \left(2 x^{2}+2 y^{2}\right)+3 x \mathrm{e}^{x y} \] a) \( \bigcirc \mathrm{df}=\left(4 \frac{x}{2 x^{2}+2 y^{2}}+3 \mathrm{e}^{x y}+3 x y \mathrm{e}^{x y}\rig
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  Find the indicated partial derivatives. \[ f(x, y)=x^{8}+2 x y^{2}-4 y ; \frac{\partial^{2} f}{\partial x^{2}} ; \frac{\partial^{2} f}{\partial y^{2}} ; \frac{\partial^{2} f}{\partial x y} \] A. \[ \b
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  the triple integral \( \iiint_{B} f(x, y, z) d V \) over the solid \( B \) \[ f(x, y, z)=1-\sqrt{x^{2}+y^{2}+z^{2}}, B=\left\{(x, y, z) \mid x^{2}+y^{2}+z^{2} \leq 25, y \geq 0, z \geq 0\right\} \]
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• differentiate plz
  \( y=\operatorname{tann}\left(\ln \sqrt{x^{2}+1}\right) \)
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• lim ( x , y ) -> ( 9 , 12 ) [( x − 7 )^ 3 − ( y − 8 ) ^3]/ x − y + 1
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  Find the following. \[ \begin{array}{l} \int\left(x^{3}+y^{4}\right) d x= \\ \int\left(x^{3}+y^{4}\right) d y= \end{array} \]
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• Evaluate the double integral. D (2x + y) dA, D = {(x, y) | 1 ≤ y ≤ 4, y − 3 ≤ x ≤ 3}
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  Evaluate the integral \( \iint_{R}\left(\frac{x}{y}-\frac{y}{x}\right) d A \) over the rectangular region, \[ R=\{(x, y) \mid 1 \leq x \leq 2,1 \leq y \leq 5\} \] \[ \iint_{R}\left(\frac{x}{y}-\frac{y
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  \[ \begin{array}{l} F_{1}(x, y)=x \mathbf{i}+\mathbf{y j} ; \quad F_{2}(\mathbf{x}, \mathbf{y})=-\mathbf{y i}+\mathbf{x} \mathbf{j} \\ F_{3}(x, y)=\frac{1}{\sqrt{x^{2}+y^{2}}}(x \mathbf{i}+\mathbf{y}
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• integracion por sustitucion trigonometrica
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  \[ \begin{array}{l} F_{1}(x, y)=x \mathbf{i}+\mathbf{y} \mathbf{j} ; \quad \mathbf{F}_{2}(\mathbf{x}, \mathbf{y})=-\mathbf{y} \mathbf{i}+\mathbf{x} \mathbf{j} ; \\ F_{3}(x, y)=\frac{1}{\sqrt{x^{2}+y^{
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  Compute \( \iiint_{R}(x+y+2 z) d V \) over the box \( B= \) \( \{(x, y, z): 0 \leq x \leq 1,0 \leq y \leq 1, \quad 0 \leq z \leq 2\} \). 2 4 6 12 13 14 26 28 32
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  Find the differential df. \[ f(x, y)=4 x \cos (y)-3 y \cos (x) \] a) \( \quad \mathrm{df}=(4 \cos (y)+3 y \sin (x)) \Delta x+(4 x \sin (y)+3 \cos (x)) \Delta y \) b) \( \mathrm{df}=(-4 x \sin (y)-3 \c
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  Find the differential df. \[ f(x, y)=\ln \left(x^{2}+4 y^{2}\right)+3 x \mathrm{e}^{x y} \] a) \( \bigcirc \mathrm{df}=\left(2 \frac{x}{x^{2}+4 y^{2}}+3 \mathrm{e}^{x y}+3 x y \mathrm{e}^{x y}\right)
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• help with c and d
  Prove the following identities. a) \( \frac{\cos x}{\sec x}+\frac{\sin x}{\csc x}=1 \) b) \( \csc x-\sin x=\cos x \cot x \) c) \( \sec t \csc t(\tan t+\cot t)=\sec ^{2} t+\csc ^{2} t \) d) \( (\tan y+
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  valuate the triple integral \( \iiint_{E} f(x, y, z) d V \) over the solid \( E \). \[ f(x, y, z)=e^{\sqrt{x^{2}+y^{2}}}, E=\left\{(x, y, z) \mid 1 \leq x^{2}+y^{2} \leq 16, y \leq 0, x \leq y \sqrt{3
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  1. \( (20, I) \) Solve the following \[ y^{\prime}+\frac{2}{x} y=5 e^{2 x}, y(1)=2 \]
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  10. (20, II) Solve the following \[ y^{\prime \prime}+y^{\prime}=3 \cos 2 x-8 e^{-x} \]
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• need help with part b
  Find each limit. \[ f(x, y)=\sqrt{y}(y+4) \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x, y)}{\D
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  Differentiate. \[ y=9 x^{2} \cos (x) \cot (x) \]
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• Find the Vector addition of A + B + C and find the magnitude and direction of the resultant vector OF THAT ADDITION
  Resuelva: Utilizando la siguente grảica de vectores en el plano cartesiano: Encuentra la suma vectorial \( \vec{A}+\vec{B}+\vec{C} \) y encuentre la magnitud y dirección del vector resultante de es
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• Solve the given differential equation. 3x^2 y ′′ + 6xy′ + y = 0.
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• Given cos(x)=-(4)/(5), choose all possible values of sin(x) from the qiven values.
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  \( y=\exp \left(\sqrt{3+7 x^{5}}\right) \)
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• Factor, if possible. Factor out the greatest common factor f 36x-4x^(3)
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• centro (1,4) eje mayor 8, extremo de eje menor (3,4) find equation
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