Calculus Archive: Questions from August 11, 2022
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\[ f(x, y)=\sqrt{x^{2}+y^{2}+25} \] Relative maximum of \( f(x, y)= \) at \( (x, y)= \) \( (\square) . \) Relative minimum of \( f(x, y)= \) at \( (x, y)= \) Saddle point of \( f(x, y)= \) at \( (x, y1 answer -
\[ f(x, y)=x^{2}+8 x y+17 y^{2}-6 y+9 \] Relative maximum of \( f(x, y)= \) at \( (x, y)=( \) Relative minimum of \( f(x, y)= \) at \( (x, y)= \) Saddle point of \( f(x, y)= \) at \( (x, y)= \) )1 answer -
1 answer
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6. Find \( \frac{d y}{d x} \) for each of the following: (a) \( y=\frac{\sqrt{x^{2}+1}-\sqrt{x^{2}-1}}{\sqrt{x^{2}+1}+\sqrt{x^{2}-1}} \) (b) \( y=x^{e}(2 x+3)^{4} \log _{7}\left(5 e^{x}\right) \) (c)1 answer -
\( \left\{\begin{array}{l}x=\sin t \\ y=\sin \pi t\end{array}, 0 \leq t \leq \pi\right. \) \( \left\{\begin{array}{l}x=\sin t \\ y=\pi \sin t\end{array}, 0 \leq t \leq \pi\right. \)0 answers -
Find all first-order partial derivatives: \[ f(w, x, y, z)=\left(42 x^{6} y^{0.42}-\sqrt[42]{x y w}+\frac{4 w z^{\frac{1}{3}} y}{x^{42}}\right)\left(\frac{0 \sin w^{0.75} y^{-3}}{\cos z}\right)\left(x1 answer -
1 answer
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Solve the differental equation. \[ \frac{d y}{d x}=8 x^{7} \sqrt{y-1} \] (a) \( y=\frac{1}{4} x^{16}+c \) (b) \( y=\left(2 x^{8}+c\right)^{2}+1 \) (c) \( y=\left(x^{8}+c\right)^{2} \) (d) \( y=\left[11 answer -
Find on equation for feel line fango st to the carve at pee point defined by the given value of \( f \). \[ x=4 \sin t, y=4 \cos t, t=\frac{3 \pi}{4} \] \( y \) (a) \( y=x-4 \sqrt{2} \) (b) \( y=4 x+43 answers -
Necesito que me explique a detalle como es el movimiento de una particula o cuerpo a partir de la función de posición. Situation: Consider a particle moving with a path given by: r(t) x(t)i +yt)j+z
Situación: Considerar una partícula que se mueve con una trayectoria dada por: \[ r(t)=x(t) i+y(t) j+z(t) k \] Discuta todo cambio en posición, velocidad y aceleración de la particula si su posici1 answer -
1 answer
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Using the following properties of a twice-differentable function \( y=f(x) \), select a possible graph of . B. c.1 answer -
2) Solve the system: \[ \begin{array}{l} x \prime=x+2 y-z, \\ y^{\prime}=x+z, \\ z^{\prime}=4 x-4 y+5 z . \end{array} \]1 answer -
1 answer
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\( \lim _{x \rightarrow \infty} \frac{\left(3 x^{5}-37\right)^{6}}{\left(x^{3}+123\right)^{10}}=9 a \) \( a \)1 answer -
(1 point) If \( g(x, y)=\ln |5 x+4 y| \), compute the following function values: \[ g(1,0)= \] \[ g(2,4)= \] \[ \begin{array}{l} g(-2,4)= \\ g(2,-4)= \\ g(-2,-4)= \\ g(t, t)= \end{array} \]3 answers -
3 answers