Calculus Archive: Questions from January 09, 2023
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Calculate \( \frac{d y}{d x} \) : a. \( y=\int_{3 x-1}^{\cos x} 1-t^{2} d t \) b. \( y=\int_{x^{2}}^{\ln x} \frac{1}{t+1} d t \) c. \( y=\ln \left(\cos \left(x^{2}+1\right)\right) \) d. \( y=e^{\sin (2 answers -
\[ y=\frac{x^{2}+2 x+1}{x+x^{2}} \] \( x=-1 \) \( \mathrm{x}=0 \) \( \mathrm{x}=0 \) and \( \mathrm{x}=-1 \) None0 answers -
Ejercicios de Práctica: Demuestre la convergencia o divergencia de las series. Si es convergente encuentre su suma. 1. \( \sum_{n=1}^{\infty}\left(1+\frac{2}{n}\right)^{n} \) 2. \( \sum_{n=0}^{\infty2 answers -
5. Determine si las siguientes funciones de \( \mathbb{R} \) en \( \mathbb{R} \) son continuas. \[ f(x)=\left\{\begin{array}{ll} -1, & x \leq 0 \\ 1, & x>0 \end{array}\right. \] \[ g(x)=\left\{\begin{2 answers -
Q3: The Chain rule. ( 20 points) a) \( y=\left(2 x^{5}+6\right)^{2} \) b) \( y=\sqrt[3]{3-8 x} \) c) \( y=\frac{5}{(2 x-3)^{2}} \) d) \( y=\left(5 x^{3}-4 x^{2}+3 x+8\right)^{-2} \)2 answers -
Q3: The Chain rule. (20 points) a) \( y=\left(2 x^{5}+6\right)^{2} \) b) \( y=\sqrt[3]{3-8 x} \) c) \( y=\frac{5}{(2 x-3)^{2}} \) d) \( y=\left(5 x^{3}-4 x^{2}+3 x+8\right)^{-2} \)2 answers