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Home Question Bank Math Calculus Archive 2024 December 19

Calculus Questions from Dec 19,2024

Browse the Calculus Q&A Archive for Dec 19,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( x \frac { \partial u } { \partial x } - y \frac { \partial u } { \partial y } = 0 \) \( x \frac { \partial u } { \partial x } - y \frac { \partial u } { \partial y } = 0 \) 5) Вычислить предел \( \lim _{x \rightarrow 0}\left(\frac{2}{\pi} \arccos x\right)^{\frac{1}{x}} \). Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.) \[ f(x)=4-3 x^{4} \] \( (x, y)=( \) Describe the concavity. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) concave downward \( \left. \begin{array} { l } { \frac { \partial u } { \partial t } = \frac { \partial _ { 0 } v _ { 0 } } { \partial x ^ { 2 } } \quad 0 < x < \pi , \quad t > 0 } \\ { u ( 0 , t ) = u ( \pi , t ) = 0 \quad t > 0 } \\ { u ( x , 0 ) = e ^ { x } \quad 0 < x < \pi } \end{array} \right. \) (25 pts.) Determine una solución formal del problema con valores iniciales y en la frontera \[ \begin{array}{ll}\frac{\partial u}{\partial t}=\frac{\partial^{2} u}{\partial x^{2}}, & 0<x<\pi, t>0 \\ u(0, t)=u(\pi, t)=0, & t>0 \\ u(x, 0)=e^{x}, & 0<x<\pi\end{array} \] Provide an appropriate response. Find the local extrema for \( f(x, y)=x^{3}-12 x+y^{2} \) Find the partial derivative. Find \( f_{x}(5,-3) \) when \( f(x, y)=7 x^{2}-9 x y \) A company manufactures and sells \( x \) pocket calculators per week. If the weekly cost and demand equations are given by: \( C(x)=8,000+5 x \) \( p=14-\frac{x}{4,000}, 0 \leq x \leq 25,000 \) Find the production level that maximizes profit. Find the absolute maximum and minimum values of the function \( f(x)=\frac{4 x}{x^{2}+1} \) on the interval \( [-3,0] \)
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