Advanced Math Archive: Questions from January 12, 2023
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HELPPPP :(
1. Find the indefinite integrals of: a) \( 3 x^{\frac{2}{3}} \) g) \( (1-2 x)^{\frac{1}{3}} \) b) \( \sqrt{(2 x)} \) h) \( \left(2 x^{2}+1\right)^{3} \) c) \( 2 x^{3}-2 x^{2}+\frac{1}{x}-2 \) i) \( \c2 answers -
Differentiate the following function: \[ y=x^{2} \sin 3 x \] Select one: \[ \begin{array}{l} \frac{d y}{d x}=2 x \sin 3 x+3 x^{2} \cos 3 x \\ \frac{d y}{d x}=6 x \sin 3 x \\ \frac{d y}{d x}=6 x \cos 32 answers -
Only part (a) (b) (e) (f)
Solve the initial value problem. (a) \( y^{\prime}=-x e^{x}, \quad y(0)=1 \) (b) \( y^{\prime}=x \sin x^{2}, \quad y\left(\sqrt{\frac{\pi}{2}}\right)=1 \) (c) \( y^{\prime}=\tan x, \quad y(\pi / 4)=32 answers -
2 answers
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2 answers
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2 answers
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2 answers
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a. Obtain the general solution by suing the method of undetermined coefficients. 1. \( y^{\prime \prime}+y^{\prime}=-\cos (x) \) 2. \( y^{\prime \prime}+9 y=18 \) 3. \( y^{\prime \prime}-6 y^{\prime}+2 answers -
Topology problem
Tema II. Sea \( \tau \) la topología de \( R \) constituida por \( \mathbf{R}, \phi \) y los intervalos infinitos abiertos \( E_{\alpha}=(a, \infty) \) i) Determine los subconjuntos cerrados de \( \t2 answers -
Using the convolution property where
c) Utilizando la propiedad de convolución donde \( L\{(f * g)(t)\}=L\{f(t)\} \bullet L\{g(t)\} \) Determinar: \( L\left\{e^{t} * \operatorname{sen}(t)\right\} \)2 answers -
2 answers
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Let \( \alpha=\sqrt[3]{2} \in \mathbb{R} \), and let \( \omega \) be a primitive cube root of unity in \( \mathbb{C} \), so \( \omega^{3}=1 \). (i) Prove that the set of all numbers \( p+q \alpha+r \a2 answers