Calculus Archive: Questions from April 12, 2023
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translation. find the critical numbers, find the relative maximum and minimums, inflexion points,concavities and graph the function.
/II. Hallar los números criticos, intervalos donde la función es creciente o decreciente. determinar máximos o minimos relativos, puntos de inflexiôn, concavidades y bosqueja la gráfica. \[ f(x)=2 answers -
Your answer will be in terms of \( h \). \[ \text { Find } \frac{f(x+h, y)-f(x, y)}{h} \text { if } f(x, y)=2 x^{2}-6 y^{2} \]2 answers -
Find the Maclaurin series of \( \sin ^{2}\left(\frac{x}{8}\right) \). Hint: \( \sin ^{2}(x)=\frac{1-\cos (2 x)}{2} \) (A) \( \sum_{n=1}^{\infty} \frac{(-1)^{n-1}(x)^{2 n}}{2^{4 n+1}(2 n) !} \) (B) \(2 answers -
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Find the Maclaurin series of \( \sin ^{2}\left(\frac{x}{4}\right) \). Hint: \( \sin ^{2}(x)=\frac{1-\cos (2 x)}{2} \) (A) \( \sum_{n=1}^{\infty} \frac{(-1)^{n}(x)^{2 n}}{2^{2 n-1}(2 n) !} \) (B) \( \s2 answers -
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2. Find the general solution to the following second-order equations: a) \[ y^{\prime \prime}+y^{\prime}=0 \] b) \[ y^{\prime \prime}-y^{\prime}=0 \] c) \[ y^{\prime \prime}+y=0 \] d) \[ y^{\prime \pr2 answers -
Find the derivative of the function \[ y=\frac{x^{2}+8 x+3}{\sqrt{x}} \] A. \( y^{\prime}=\frac{3 x^{2}+8 x-3}{x} \) B. \( y^{\prime}=\frac{3 x^{2}+8 x-3}{2 x^{3 / 2}} \) C. \( y^{\prime}=\frac{2 x+8}2 answers -
Find \( \frac{\mathrm{dy}}{\mathrm{dt}} \). \[ y=\cos (\sqrt{8 t+11}) \] A. \( -\frac{1}{2 \sqrt{8 t+11}} \sin (\sqrt{8 t+11}) \) B. \( -\sin (\sqrt{8 t+11}) \) C. \( -\frac{4}{\sqrt{8 t+11}} \sin (\s2 answers -
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5. \( \sum_{k=1}^{\infty} \frac{5^{k-1}-3^{k-1}}{8^{k-1}}= \) (A) \( \frac{1}{3} \) (B) \( \frac{16}{15} \) (C) \( \frac{49}{24} \) (D) \( \frac{34}{15} \)2 answers -
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Evaluate the triple integral \( \iiint_{Q} f(x, y, z) d V \). \[ \begin{array}{l} f(x, y, z)=3 x+3 y-10 z, Q=\{(x, y, z) \mid 0 \leq x \leq 8,-7 \leq y \leq 7,1 \leq z \leq 9 \\ \iiint_{Q} f(x, y, z)2 answers -
x=[[k,0],[0,2]]i=[[1,0],[0,1]]encontrar los valores que hagan verdadera la igualdad x^(2)-(5)/(2)x+i0 answers
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Encuentra el producto más grande que pueden tener los números positivos x, y y z si x + y + z2 = 16.1 answer
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