(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)

I've been working on this for a few days and i just don't understand, it's due in a few hours. you. the direction of a vector is defined as the angle of the vector in relation to a horizontal line. as a standard, this angle is measured counterclockwise from the positive x-axis. the direction or angle of v in the diagram is α. part a: how can you use trigonometric ratios to calculate the direction α of a general vector v = < x, y> similar to the diagram? part b suppose that vector v lies in quadrant ii, quadrant iii, or quadrant iv. how can you use trigonometric ratios to calculate the direction (i. e., angle) of the vector in each of these quadrants with respect to the positive x-axis? the angle between the vector and the positive x-axis will be greater than 90 degrees in each case. part c now try a numerical problem. what is the direction of the vector w = < -1, 6 > ?