Calculus Archive: Questions from April 01, 2023
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GIVEN: \( f: D \subset \mathbb{R}^{2} \rightarrow \mathbb{R}, f(x, y)=\sin ^{2} x \cos y \) and \( D=\left\{(x, y) \mid \begin{array}{ll}0 \leq x \leq \frac{\pi}{2} \\ 0 \leq y \leq 2 x\end{array}\rig2 answers -
please answer all!
Find all the second partial derivatives. \[ \begin{array}{l} f(x, y)=x^{6} y^{6}+2 x^{5} y \\ f_{x x}(x, y)= \\ f_{x y}(x, y)= \\ f_{y x}(x, y)= \\ f_{y y}(x, y)= \end{array} \] Find the first partia2 answers -
indifinite Derivatives please help fast
\( \begin{array}{c}y=\cos x \cdot\left(2 x^{3}+5\right) \\ y=\tan ^{2}\left(\sin \left(\theta^{4}\right)\right)\end{array} \)2 answers -
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Solve differential equations
1. Solve \[ \left\{\begin{array}{l} t^{2} \cdot \frac{d x}{d t}=x^{3}-2 x t \\ x(1)=1 \end{array}\right. \] 2. Solve \[ \left(2 x^{5}-3 x y\right) d y+\left(5 x^{4} y-y^{2}\right) d x=0 \] 3. Solve \[2 answers -
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Find the limit, if it exists. \[ \lim _{(x, y) \rightarrow(1,2)}\left(x^{5}+4 x^{3} y-5 x y^{2}\right) \] A. \( \lim _{(x, y) \rightarrow(1,2)} f(x, y)=10 \) B. \( \lim _{(x, y) \rightarrow(1,2)} f(x,2 answers -
1) Evaluate \[ \int \frac{1}{x^{2}} \cos \left(\frac{1}{x}\right) d x \] (A) \( \frac{1}{x} \sin \left(\frac{1}{x}\right) \) (B) \( -\frac{1}{x} \sin \left(\frac{1}{x}\right)+C \) (C) \( \sin \left(\f2 answers