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Calculus Archive: Questions from August 13, 2022

• ASAP PLEASE!
  \( y^{\prime}=\left(x^{2}-4\right)(3 y+2), y(0)=0 \)
  3 answers

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  \( \mathbf{r l}(\mathbf{F} \times \mathbf{G})=\nabla \times(\mathbf{F} \times \mathbf{G}) \) \( \mathbf{F}(x, y, z)=\mathbf{i}+8 x \mathbf{j}+4 y \mathbf{k} \) \( \mathbf{G}(x, y, z)=x \mathbf{i}-y \m
  1 answer

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  \( \operatorname{liv}(\mathbf{F} \times \mathbf{G})=\nabla \cdot(\mathbf{F} \times \mathbf{G}) \) \( \mathbf{F}(x, y, z)=\mathbf{i}+6 x \mathbf{j}+8 y \mathbf{k} \) \( \mathbf{G}(x, y, z)=x \mathbf{i}
  1 answer
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  (20 pts) Differentiate the function by using rules. (a) \( y=\frac{1}{2 x-3} \) (b) \( y=\ln (7 x+5) \) (c) \( y=3 x^{3} e^{5 x} \) (d) \( y=\pi x+\pi^{5} \)
  1 answer
• Find d2y dx2 in terms of x and y. y4 = x7
  3 answers
• Find d2y dx2 in terms of x and y. x2y2 − 10x = 7
  1 answer
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  Find the derivative of the function. \[ y=\frac{x^{2}-3 x+2}{x^{7}-2} \] A. \( y^{\prime}=\frac{-5 x^{8}+18 x^{7}-14 x^{8}-4 x+6}{\left(x^{7}-2\right)^{2}} \) B. \( y^{\prime}=\frac{-5 x^{8}+18 x^{7}-
  1 answer
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  \( t=-\frac{35 \pi}{6} \) corresponds to the point \( (x, y)= \) \( t=\frac{19 \pi}{6} \) corresponds to the point \( (x, y) \)
  1 answer

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  Find the gradient field of \( f(x, y)=\frac{1}{6}(e x-6 y)^{2} \)
  1 answer
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  Find the \( \iiint_{Q} f(x, y, z) d V \) A. \( Q=\left\{(x, y, z) \mid\left(x^{2}+y^{2}+z^{2}=4\right.\right. \) and \( \left.z=x^{2}+y^{2}, f(x, y, z)=x+y\right\} \) B. \( \mathrm{Q}=\left\{(x, y, z)
  1 answer
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  Determine \( h=h(x, y) \) so that \( \frac{\partial f}{\partial x}=\frac{h(x, y)}{\left(4 x^{2}+2 y^{2}\right)^{2}} \) 1. \( h(x, y)=16 x y^{2} \) 2. \( h(x, y)=16 x y^{3} \) when \( f(x, y)=\frac{4 x
  3 answers
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  Determine \( f_{x x} f_{y y}-\left(f_{x y}\right)^{2} \) when 1. \( f_{x x} f_{y y}-\left(f_{x y}\right)^{2}=12 x-4 \) \( f(x, y)=x^{3}+2 y^{2}+2 x+6 y+2 x y . \) 2. \( f_{x x} f_{y y}-\left(f_{x y}\r
  3 answers
• c please
  Find the \( \iiint_{Q} f(x, y, z) d V \) A. \( Q=\left\{(x, y, z) \mid\left(x^{2}+y^{2}+z^{2}=4\right.\right. \) and \( \left.z=x^{2}+y^{2}, f(x, y, z)=x+y\right\} \) B. \( \mathrm{Q}=\left\{(x, y, z)
  0 answers