Calculus Archive: Questions from May 22, 2023
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Find an expression for \( d y / d x \). 11) \( \mathrm{y}=\frac{3}{\mathrm{u}^{2}} \) and \( \mathrm{u}=8 \mathrm{x}-5 \) A) \( -\frac{48}{(8 x-5)^{3}} \) B) \( -\frac{48}{8 x-5} \) C) \( -\frac{24}{82 answers -
(iv) \( \int_{1}^{2} \int_{y}^{y^{2}} d x d y \) \( \nu(\mathrm{v}) \quad \int_{0}^{1} \int_{0}^{1} \frac{y}{1+x y} d x d y \)2 answers -
\( \begin{array}{l}\iint_{D}\left(2+x^{2} y^{3}-y^{2} \sin x\right) d A, \\ D=\{(x, y)|| x|+| y \mid \leqslant 1\}\end{array} \)2 answers -
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5.) Solve the problem: y" - y = ex when y(0) = 0 and y'(0) = 0.
5.) Solve the problem: \[ y^{\prime \prime}-y=e^{x} \quad \text { when } y(0)=0 \quad \text { and } y^{\prime}(0)=0 \]2 answers -
Q7 Assuming y = f(x), compute[3xy²] dx d=34² зуг Q8 Compute the following derivatives: (a) = [e5x²-7x] dx Q9 Integrate the following: (a) √5x(x²-3x + 1)dx (b) S(12e4x - 7+2) dx Q10 Compute 2
Q7 Assuming \( y=f(x) \), compute \( \frac{d}{d x}\left[3 x y^{2}\right] \) \[ \begin{array}{l} \frac{d}{d x}=3 y^{2} \\ \left(3 x \cdot y^{2}\right)=3 x \cdot 2 x+\left(y^{2}\right) \cdot(3) \\ = \en2 answers -
\[ \lim _{x \rightarrow 1} \frac{x^{3}-6 x^{2}+5}{x-1} \] solve The initial Ualue Problem \[ y^{\prime}+y=2 e^{x}: y(0)=11 \]2 answers -
Calcule el centroide (Xc,Yc) de la porción sombreada de la siguiente figura plana. No tenga en cuenta el material sino la figura plana. s=6 . Calcule el centro de gravedad (Xcg, Ycg) de la figura
Calcule el centroide \( \left(X_{\mathrm{c}}, Y_{c}\right) \) de la porción sombreada de la siguiente figura plana. No tenga en cuenta el material sino la figura plana.[valor 35 puntos Calcule el cen2 answers -
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