B

1003047402

Level: 
B
Choose the best first step to simplify and calculate the limit of the following sequence. \[ \left(\frac{3\cdot5^n+2\cdot6^n}{2\cdot5^n+4\cdot6^n}\right)_{n=1}^{\infty} \]
We take \( 6^n \) outside the brackets in the numerator and the denominator.
We take \( 5^n \) outside the brackets in the numerator and denominator.
We divide the numerator and denominator by \( 5^n \).
We divide the numerator by \( 6^n \).
We divide the denominator by \( 6^n \).

1003047401

Level: 
B
Choose the correct formula to calculate the limit. \[ L=\lim\limits_{n\rightarrow\infty}\frac{3\cdot5^n+2\cdot6^n}{2\cdot5^n+4\cdot7^n } \]
\( L=\lim\limits_{n\rightarrow\infty}⁡ \frac{3\cdot\left(\frac57\right)^n+2\cdot\left(\frac67\right)^n}{2\cdot\left(\frac57\right)^n+4} =0 \)
\( L=\lim\limits_{n\rightarrow\infty}⁡\frac{3\cdot\left(\frac56\right)^n+2}{2\cdot\left(\frac57\right)^n+4}=\frac12 \)
\( L=\lim\limits_{n\rightarrow\infty}⁡\frac{3+2\cdot\left(\frac65\right)^n}{2+4\cdot\left(\frac75\right)^n } =\frac32 \)
\( L=\frac{3\cdot5^{\infty}+2\cdot6^{\infty}}{2\cdot5^{\infty}+4\cdot7^{\infty}}=\infty \)
\( L=\lim\limits_{n\rightarrow\infty}⁡\frac{3\cdot\left(\frac57\right)^n+2\cdot\left(\frac67\right)^n}{2\cdot\left(\frac57\right)^n+4\cdot\left(\frac77\right)^n}=\frac56 \)

1103118504

Level: 
B
Given the next graph of a logarithmic function \( f \), choose the correct list of properties of \( f \).
decreasing, asymptote at \( x=0 \), unbounded
decreasing, asymptote at \( y=0 \), unbounded
decreasing, asymptote at \( x=0 \), bounded below
increasing, asymptote at \( y=0 \), bounded below

1003023307

Level: 
B
The radian measure of the angle \( \theta \) is \( \frac{\pi}3 \). How many values from the set \( M = \left\{\frac43\pi, \frac73\pi, \frac83\pi, \frac{13}3\pi, -\frac53\pi, \frac{61}3\pi, -\frac{61}3\pi \right\} \) are the measures of angles coterminal to \( \theta \)? (Two angles are coterminal if they are drawn in the standard position and both have their terminal sides in the same location.)
\( 4 \)
\( 5 \)
\( 6 \)
\( 3 \)