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Calculus Archive: Questions from January 02, 2023

• Determine which of the following series converges
  Determinar cuál de las siguientes series converge. \[ \begin{array}{l} \sum_{n=1}^{\infty}\left(4+(-1)^{n}\right)^{n} \\ \sum_{n=0}^{\infty} 5\left(\frac{3}{2}\right)^{n} \\ \sum_{n=1}^{\infty} \frac
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• If the series n=1ªn is conditionally convergent, determine which of the following series is divergent
  Si la serie \( \sum_{n=1}^{\infty} a_{n} \) es condicionalmente convergente, determine cuál de las siguientes series es divergente. \[ \begin{array}{l} \sum_{n=1}^{\infty}\left(a_{n}\right)^{2} \\ \s
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• 3.Find a power series centered c=-3 for the function f(x)=1/2x-5
  3. Hallar una serie de potencias centradaen \( c=-3 \) para la función \( f(x)=\frac{1}{2 x-5} \) a) \( \sum_{n=0}^{\infty}-\frac{(3 x)^{n}}{2^{n+1}} \) b) \( \sum_{n=0}^{\infty}-\frac{2^{n}(x-3)^{n}
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• 4) For the power series , find the interval of convergence
  4) Para la serie de potencias \( \sum_{n=0}^{\infty} \frac{(x-2)^{n+1}}{(n+1) 4^{n+1}} \), halla el intervalo de convergencia. a) \( (-2,6) \) b) \( [-2,6] \) c) \( (-2,6] \) d) \( [-2,6) \) e) Ningun
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• can you help me with this. please have good explanation and handwritinf
  Chain Rule: Natural Logs and Exponentials Date Differentiate each function with respect to \( x \). 1) \( y=\ln x^{4} \) 2) \( y=\ln x^{2} \) 3) \( y=\ln 5 x^{3} \) 4) \( y=\ln 2 x^{5} \) 5) \( y=\ln
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  Evaluate the following triple integrals: a) \( \quad \int_{1}^{2} \int_{0}^{2 z} \int_{0}^{\ln x} x e^{-y} d y d x d z \) b) \( \quad \iiint_{E} 2 x d V, E=\left\{(x, y, z) \mid 0 \leq y \leq 2,0 \leq
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  5. Evaluate \( \iint_{D} 42 y^{2}-12 x d A \) where \( D=\left\{(x, y) \mid 0 \leq x \leq 4,(x-2)^{2} \leq y \leq\right. \) \( 6\} \).
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  Compute the limit \( \quad \lim _{n \rightarrow \infty} \sum_{k=1}^{2 n}(-1)^{k}\left(\frac{k}{2 n}\right)^{111} \)
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