Calculus Archive: Questions from August 14, 2022
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Find dy/dx.
5. \( y=5^{\sin \left(x^{2}\right)} \log \left(1-3 x^{4}\right) \) find \( \frac{d y}{d x} \) 6. \( y=5^{3 x} \cot \left(2 x^{3}\right) \) find \( \frac{d y}{d x} \) 7. \( y=e^{x^{2}} \sec ^{3}(3 x) \1 answer -
(5 points) Find the partial derivatives of the function \[ f(x, y)=x y e^{1 y} \] \( f_{x}(x, y)= \) \( f_{y}(x, y)= \) \( f_{3} \) \( f_{y} \)1 answer -
(5 points) Find the partial derivatives of the function \[ f(x, y)=\int_{y}^{x} \cos \left(3 t^{2}+7 t-6\right) d t \] \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \end{array} \]3 answers -
\( y=f(x) \) and \( \frac{y}{x^{2}}+\frac{x}{y^{2}}=2 x y \), find \( y^{\prime} \) at point \( (1,1) \)1 answer -
1 answer
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6) Solve the IVP \( y^{\prime \prime}+9 y=t \mathcal{V}_{2}(t), \quad y(0)=0, \quad y^{\prime}(0)=0 \)3 answers -
consider the following graph to find the limits in function as requested
\[ \begin{array}{l} \lim _{x \rightarrow-2^{-}} f(x)= \\ \lim _{x \rightarrow-2^{+}} f(x)= \\ \lim _{x \rightarrow 0} f(x)= \end{array} \] 5) \( \lim _{x \rightarrow-2} f(x)= \) 6) \( \lim _{x \righta1 answer -
Find the gradient vector field \( (\vec{F}(x, y, z)) \) of \( f(x, y, z)=x \cos \left(\frac{z}{y}\right) \). \[ \vec{F}(x, y, z)= \]3 answers -
1 answer
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plz help thanks
Given \( f(x, y)=-2 x^{5}-6 x y^{4}+3 y^{6} \) \[ f_{x}(x, y)= \] \[ f_{y}(x, y)= \]1 answer -
plz help thanks
Given \( f(x, y)=-2 x^{6}+4 x y^{3}+3 y^{4} \) \( f_{x x}(x, y)= \) \( f_{x y}(x, y)= \)1 answer