Calculus Archive: Questions from December 28, 2022
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2. Determine cuál de las siguientes series converge \[ \begin{array}{l} \sum_{n=1}^{\infty} \frac{1}{n} \\ \sum_{n=0}^{\infty} 3\left(\frac{4}{3}\right)^{n} \\ \sum_{n=0}^{\infty} \frac{1}{n^{0.3}} \2 answers -
Find each limit. \[ f(x, y)=4 x^{2}+6 y^{2} \] (a) \( \lim _{\Delta x \rightarrow 0} \frac{f(x+\Delta x, y)-f(x, y)}{\Delta x} \) (b) \( \quad \lim _{\Delta y \rightarrow 0} \frac{f(x, y+\Delta y)-f(x2 answers -
13. Find \( \frac{d y}{d x} \) if (a) \( y=\int_{1}^{x} \frac{1}{t} d t, \quad x>0 \) (b) \( y=\int_{\sqrt{x}}^{0} \sin t^{2} d t \) (c) \( y=\left(\int_{x^{2}}^{x}\left(t^{3}+1\right)^{10} d t\right)2 answers -
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Complete the table. [-/1 Points] LARCALCET7 3.4.010. Complete the table.2 answers -
Given that \( 3 x-\tan y=4 \), what is \( \frac{d y}{d x} \) in terms of \( y \) ? (A) \( \frac{d y}{d x}=3 \sin ^{2} y \) (B) \( \frac{d y}{d x}=3 \cos ^{2} y \) (C) \( \frac{d y}{d x}=3 \cos y \cot2 answers