At the beginning of an experiment, a scientist has 260 grams of radioactive goo. After 210 minutes, her sample has decayed to 8.125 grams. What is the half-life of the goo in minutes? 42 Find a formula for \( G(t) \), the amount of goo remaining at time \( t \). \( G(t)=260 e^{-0.0165 t} \) How many grams of goo will remain after 47 minutes? You may enter the exact value or round to 2 decimal places.

\( \lim _ { z - 1 } \frac { 4 z + 3 } { 2 z + 1 } \)

Jika \( m \) dan \( n \) adalah bilangan negatif dan berlaku \( \lim _{x \rightarrow n} \frac{4-\sqrt{m(x+n)}}{n-x}=n \), maka nilai dari \( m-n=\cdots \) (A) -9 (B) -7 (C) -5 (D) 7 (E) 9

\( f ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } - x - 1 , x = - 1 \)

4. Let \( g \) be a function such that \( g(1)=3 \) and whose derivative is \( g^{\prime}(x)=6 \cos (2 \pi x)+3 \). Solve analytically a. Use a linear approximation to estimate the value of \( g(1.2) \). b. Find the solution to the differential equation \( d g=(6 \cos (2 \pi x)+3) d x \)

23-24 ¿Cómo podría "remover la discontinuidad" en cada una de las siguientes funciones? En otras palabras, ¿cómo redefiniría \( f(2) \) a fin de que sean continuas en \( x=2 \) ? \( \begin{array}{ll}\text { 23. } f(x)=\frac{x^{2}-x-2}{x-2} & \text { 24. } f(x)=\frac{x^{3}-8}{x^{2}-4}\end{array} \)