(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)

At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. the cyclic nature of wind and moving sand determines the shape and location of large dunes. at a test site, the prevailing direction of the wind did not change noticeably. however, the velocity did change. fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. based on long-term experience, σ can be assumed to be 245 cm/sec. (a) find a 95% confidence interval for the population mean wind speed at this site. (round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec