Let \( f(x) \) and \( g(x) \) be two functions that are continuous on the interv \( -1 \leq x \leq 2 \) and satisfy: \( \int_{-1}^{2} f(x) d x=3 \quad \int_{-1}^{2} g(x) d x=2 \quad \int_{0}^{2} f(x) d x=1 \) Compute the following integrals: (1) \( \int_{-1}^{2}(f(x)-3 g(x)) d x \) (2) \( \int_{-1}^{0} f(x) d x+\int_{2}^{-1} g(x) d x \)

Consider the following. \[ \begin{array}{l}y=x^{2} \\ y \\ y \\ y\end{array} \] (b) Use the integration capabilities of the graphing utility to approximate the area to four de

Ejercicio 1. Determina la derivada de cada una de las siguientes funciones. 1. \( f(x)=10^{x} \) 2. \( f(x)=14^{x}-4^{x} \) 3. \( f(x)=9^{x}+2^{x} \) 4. \( f(x)=6^{x} \) 5. \( f f(x)=\log _{6} x \) 6. \( f(x)=\log _{15} x+3 \log _{20} x-5 \log _{2} x \) 7. \( f(x)=4 \operatorname{sen} x-5 \cos x \) 8. \( f(x)=6 \tan x-6 \csc x-3 \cos x \) 9. \( f(x)=\cos x-4 \tan x \) 10. \( f(x)=4 \sec x+5 \cot x \)

\( \lim _ { m \rightarrow + \infty } m [ 2 - \sin ( n ^ { 2 } + 1 ) ] \)

Find the Maclaurin series for the following function and determine its radius of convergence \( R \). \( f(x)=\ln \left(\frac{1+x}{1-x}\right) \). \( R=\square \) Use the first four terms of the series to approximate \( \ln (3) \). (Round your answer to six decimal places.) \( \ln (3) \approx \square \)

Round your answers to the nearest thousandth. Do not round any intermediate computations. \[ \ln \frac{3}{4}=\square \] \( \ln 20.6=\square \)