(1 pt) let an=n+1n+3. find the smallest number m such that: (a) |an−1|≤0.001 for n≥m m= 1997 (b) |an−1|≤0.1 for n≥m m= 23 (c) now use the limit definition to prove that limn→[infinity]an=1. that is, find the smallest value of m (in terms of t) such that |an−1|m. (note that we are using t instead of ϵ in the definition in order to allow you to enter your answer more easily). m= 2/t - 3t (enter your answer as a function of t)

Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2

In tossing one coin 10 times, what are your chances for tossing a head? a tail? 2. in tossing one coin 100 times, what are your chances for tossing a head? a tail? 3. in tossing one coin 200 times, what are your chances for tossing a head? a tail? deviation = ((absolute value of the difference between expected heads and observed heads) + (absolute value of the difference between expected tails and observed tails)) divided by total number of tosses. this value should always be positive. 4. what is the deviation for 10 tosses? 5. what is the deviation for the 100 tosses? 6. what is the deviation for 200 tosses? 7. how does increasing the total number of coin tosses from 10 to 100 affect the deviation? 8. how does increasing the total number of tosses from 100 to 200 affect the deviation? 9. what two important probability principles were established in this exercise? 10. the percent of occurrence is the obtained results divided by the total tosses and multiplied by 100%. toss the coins 100 times and record your results. calculate the percent occurrence for each combination. percent head-head occurrence: percent tail-tail occurrence: percent head-tail occurrence:

What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = + x 2 6 10 12