Advanced Math Archive: Questions from March 08, 2023
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(g) \( \frac{\cos 2 \theta}{1+\sin 2 \theta}=\tan \left(\frac{\pi}{4}-\theta\right) \) (h) \( 8 \cos ^{3} 40^{\circ}=6 \cos 40^{\circ}-1 \) (i) \( \tan \left(\frac{\pi}{4}+\theta\right)-\tan \left(\fr2 answers -
2 answers
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2 answers
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Find the probability that the pair (x, y) satisfies y <= 1/2x.
\( f(x, y)=\left\{\begin{array}{ll}c e^{x^{2}} & \text { if }(x, y) \in[0,1] \times[0,1] \text { and } y \leq x \\ 0 & \text { otherwise }\end{array}\right. \)2 answers -
Exercise 4: Solve the IVPs using the Laplace transform: h) \( y^{\prime \prime}-y^{\prime}-6 y=0, y(0)=11, y^{\prime}(0)=28 \) i) \( \quad y^{\prime \prime}-4 y^{\prime}+4 y=0, y(0)=8.1, y^{\prime}(0)2 answers -
What is the derivative of the function \( y=x^{2} \sin \frac{x}{2} \cos \frac{x}{2} \) ? \[ y^{\prime}=x \sin x+\frac{1}{2} x^{2} \cos x \] \[ y^{\prime}=x \sin x+x^{2} \cos x \] \[ y^{\prime}=\frac{12 answers -
answer 42 and 43 quickly
No Limit Exists at the Origin By considering different paths of approach, show that the functions in Exercises 41-48 have no limit as \( (x, y) \rightarrow(0,0) \). 41. \( f(x, y)=-\frac{x}{\sqrt{x^{22 answers -
\[ \begin{array}{ll} \mathbf{x}_{1}=\left[\begin{array}{r} -1 \\ 2 \\ 3 \end{array}\right], & \mathbf{x}_{2}=\left[\begin{array}{l} 3 \\ 4 \\ 2 \end{array}\right], \\ \mathbf{x}=\left[\begin{array}{l}2 answers -
Sabemos que: \( \int_{0}^{+\infty} \frac{\operatorname{Sin}(a x)}{x} d x=\frac{\pi}{2} \) Usando trigonometria elemental, muestre que: b) \( \frac{2}{\pi} \int_{0}^{+\infty} \frac{\operatorname{Sin}[x0 answers -
2 answers
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2 answers
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discrete mathematics
Solve by variation of parameters: \[ y^{\prime \prime}-9 y=\frac{1}{1+e^{-3 t}}, \] \[ y^{\prime \prime}-2 y^{\prime}+17 y=\frac{e^{t}}{\cos 4 t} \] \[ y^{\prime \prime}-4 y^{\prime}+4 y=\frac{e^{2 t}2 answers -
If \( y=\frac{u^{3}}{u+2} \) and \( u=\sqrt{x^{2}+5} \) determine \( \frac{d y}{d x} \) when \( x=1 .-2 \)2 answers -
Prove that \[ \left(\frac{1+i \tan \theta}{1-i \tan \theta}\right)^{n}=\frac{1+i \tan n \theta}{1-i \tan n \theta} \]2 answers -
2 answers
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Determine el dominio de convergencia de la siguiente serie de potencias \[ \sum_{n=1}^{\infty}(-1)^{n+1} n^{-9} 9^{-n}(x+9)^{n} \]2 answers -
Exercise 4: Solve the IVPs using the Laplace transform: h) \( \quad y^{\prime \prime}-y^{\prime}-6 y=0, y(0)=11, y^{\prime}(0)=28 \) i) \( \quad y^{\prime \prime}-4 y^{\prime}+4 y=0, y(0)=8.1, y^{\pri2 answers -
Sea la función \[ f(z)=\frac{z+2}{2 z-1} \] determine (a) El conjunto de puntos \( z \) cuya imagen es \( w=2+3 i \) (b) El conjunto de puntos \( z \) cuya imagen es \( w=\frac{4-8 i}{5} \)2 answers -
Utilice el Teorema de Cauchy-Goursat, donde \( C \) es la circunferencia \( |z|=\pi \) para evaluar la integral \[ \oint_{C}(1+z)^{1 / z} d z \]2 answers