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Calculus Archive: Questions from September 01, 2022

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  Given \( f(x, y)=\sqrt{3 x^{5} y-7 x^{3} y} \), fil \( f_{x}(x, y)= \) \[ f_{y}(x, y)= \]
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  cotisiera la risistincia def arre y fetermanes (4 petcia) a. La futicion vectorial igat delietibe la pricton det proyectit. b. Las dcuaciones pararnatricas pae desariber el thowenicnto d. \( 1-4 \) al
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• Determine the length of the arc at the given interval
  I. Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \)
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• ln (y + 1) – ln 3 = x + ln x Solve for y.
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  \[ \int \frac{3 x}{\sqrt{x}} d x= \] Seleccione una: a. \( 3 x^{\frac{5}{2}}+C \) b. \( x^{\frac{7}{2}}+C \) c. \( 2 x^{\frac{3}{2}}+C \) d. \( \frac{6}{5} x^{\frac{5}{2}}+C \) \[ \int\left(\frac{3 x
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• true or false ?
  \[ \int \frac{1}{1+x^{2}} d x=\ln \left(1+x^{2}\right)+C \] Seleccione una: a. Cierto b. Falso \[ \int\left(e^{x}-2 x+\cos (x)\right) d x= \] Seleccione una: a. \( e^{x}-x^{2}+\cos (x)+C \) b. \( e^{
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  \[ \int 3 x \sqrt{x} d x \] Seleccione una: a. \( 2 x^{\frac{3}{2}}+C \) b. \( x^{\frac{7}{2}}+C \) c. \( 3 x^{\frac{5}{2}}+C \) d. \( \frac{6}{5} x^{\frac{5}{2}}+C \)
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  4. If \( f(x, y, z)=e^{x y} \ln z \), then find the following partial derivatives: (1) \( f_{x}(x, y, z) \) (2) \( f_{y}(x, y, z) \) (3) \( f_{z}(x, y, z) \)
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  \[ \text { Using the function } f(x)=\left\{\begin{array}{lll} 3-x^{2} & \text { If } & x
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• Determine the length of the arc in the given interval
  Determine la longitud del arco en el intervalo dado a) \( r(t)=i+t^{2} j+t^{3} k ;[0,2] \) b) \( r(t)=\langle 4 t,-\cos t, \operatorname{sen} t\rangle ;\left[0, \frac{3 \pi}{2}\right] \)
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  3. Solve the following differential equations: (a) \[ 2 \frac{d y}{d x}=\frac{3}{x^{2}+x-2}, \quad y(0)=1 \] 1 (b) \[ \frac{d y}{d x}=\sin (2 x)-y \tan (x)-1, \quad y(0)=-1 . \] (c) \[ y^{\prime \prim
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  Find \( \frac{\partial z}{\partial x} \) and \( \frac{\partial z}{\partial y} \) if \( z=f(x, y)=x^{2} y^{3} \sin (x-2 y) \) \[ \begin{array}{l} \frac{\partial z}{\partial x}=2 x y^{3} \sin (x-2 y)+x^
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  Differentiate the function. \[ y=\left(4 x^{4}-x+1\right)\left(-x^{5}+3\right) \] \[ y^{\prime}= \]
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  Differentiate the following function. \[ f(x)=x^{2} e^{x} \] A) \( f^{\prime}(x)=2 x e^{x} \) B) \( f^{\prime}(x)=x e^{x}(x+2) \) c) \( f^{\prime}(x)=x^{2} e^{x}-2 x e^{x} \) D) \( f^{\prime}(x)=2 x e
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  Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=x \) and \( R=[5,10] \times[-2,1] \) \( \iint_{R} f(x, y) d A= \)
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  If \( y=\log _{10}\left(x^{3}+14\right) \), find \( d y / d x \)
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  If \( y=\left(x^{4}+2\right)^{\sin (2 x)} \), find \( d y / d x \)
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• PLEASEE HELPP ASAPPP
  Consider the piecewise function \[ P(x)=\left\{\begin{array}{l} x+1 \text { if } x \leq 3 \\ -x \text { if } x>3 \end{array}\right. \] \[ P(1)= \] \[ P(2.99)= \] \[ P(3)= \] \[ P(3.01)= \]
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  Find \( \iint_{R} f(x, y) d A \) where \( f(x, y)=x \) and \( R=[5,9] \times[1,6] \). \( \iint_{R} f(x, y) d A= \) Evaluate the double integral of the function over the rectangle : \[ \iint_{\mathcal
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