UESTION 3 On the interval \( [-2,3] \), the maximum vertical distance between the line \( y=x+6 \) and the parabola \( y=x^{2} \) is equal to

11 My computer has a program that can work out the decimal value of \( \pi \) to a large numbers of digits. You can specify the number of digits required. The time it takes is directly proportional to the square of the number of digits specified. The computer can work out \( \pi \) to 5000 significant figures in exactly half a second. a) Find a formula for the number of digits, \( n \), that the computer can work out in \( t \) seconds. b) Use the formula to find out how long it would take to calculate \( \pi \) to one million digits. c) How many digits can the computer work out in 10 minutes?

\( y = \frac { \sqrt { 2 x - 1 } } { 3 x ^ { 2 } - 1 } \quad [ \frac { 1 } { 2 } \leq x \)

Consider the following piecewise-defined function. \[ f(x)=\left\{\begin{array}{ll}\frac{-5}{x+3} & \text { if } x<-3 \\ -9 & \text { if } x=-3 \\ -x^{2}+4 & \text { if } x>-3\end{array}\right. \] Step 2 of 3 : Evaluate this function at \( x=-3 \). Write the exact answer. Do not round. If the answer is undefined, write Und as your answer. Answer \( f(-3)= \)

Below is the graph of \( y=\ln x \). Translate it to become the graph of \( y=\ln (x-3)-2 \).

2. Esboce o gráfico da função \( f:[0,3] \longrightarrow[-2,10] \) dada por \( f(x)=x^{2}+x-2 \). Verifique se \( f \) é invertível. Se o for, determine sua inversa \( f^{-1} \). 3. Mostre que dentre todos os retângulos de mesmo perímetro o de maior área é o qua- drado.