Use the theorems proved in class about induction to evaluate the sums below. (Note that you are begin asked to apply the theorems, not formally proving a new theorem.) a. \( 7+14+21+28+\cdots+350^{\circ} \) b. \( 16+17+18+\cdots+411 \) c. \( 1-\frac{1}{10}+\frac{1}{100}-\frac{1}{1000} \cdots+\frac{1}{10^{18}} \)

State the equation of \( f(x) \) if its domain is \( \{x \in R \mid x \neq 0\} \), the \( y \)-intercept does not exist, and the equation of the horizontal asymptote is \( y=1 \).

A weight attached to a spring is at its lowest point, 9 inches below equilibrium, at time \( t=0 \) seconds. When the weight it released, it oscillates and returns to its original position at \( t=3 \) seconds. Which of the following equations models the distance, \( d \), of the weight from its equilibrium after \( t \) seconds? \( d=-9 \cos \left(\frac{\pi}{3} t\right) \) \( d=-9 \cos \left(\frac{2 \pi}{3} t\right) \) \( d=-3 \cos \left(\frac{\pi}{9} t\right) \) \( d=-3 \cos \left(\frac{2 \pi}{9} t\right) \)

State the equation of \( f(x) \) if its domain is \( \{x \in R \mid x \neq 0\} \), the \( y \)-intercept does not exist, and the equation of the horizontal asymptote is \( y=1 \).

e domain of the function \( f: f(x)=\sqrt{16-x^{2}} \)

State the equation of \( f(x) \) if the vertical asymptote is \( x=3 \), the horizontal asymptote is \( y=1 \), the \( x \)-intercept is \( (0,0) \) and the \( y \)-intercept is \( (0,0) \).