MAT 210 Test 2 Page 1. [4 pts each] Find the following limits (if they exist):(a)282lim23xxxx (b)41lim34xxx(c)4212828lim32xxxxx(d)xxe 5310lim2. Let 0 ,20 ,20 ,2)(2xxxxxxfA. [4 pts each ] Find the following limits:(a))(lim0xfx(b))(lim0xfx(c))(lim0xfxS01A Copyright 2001 Department of Mathematics Arizona State University2MAT 210 Test 2 Page (Question 2 continued)B. [5 pts] Use the definition of 'continuity of a function at a point' to determine whether the piecewise function, )(xf, given above, is continuous at 0x? 3. Let 245)( xxxf . (a) [6 pts] Find f '(x) using the limit definition of f '(x). (b) [6 pts] Use your answer to part (a) to find the equation of the tangent line to f(x) at the point (2, f (2)).4. [5 pts each] Find the derivatives of the following functions:(a)xexxxf2381423)( (b)xxxxg 23ln25)(7S01A Copyright 2001 Department of Mathematics Arizona State University3MAT 210 Test 2 Page (Question 4 continued)(c)823)223()( xxxxh(d))78ln()(34xxxxp (e)xexxq3.053)(5. The number of computers connected to the Internet, N , in millions, can beapproximated by the exponential function ,)58.2(0712.0)(ttN  where t is in years and t = 0 corresponds to 1989.(a) [6 pts] Find the average rate of change of the number of computers connected to the Internet from 1990 to 1995. (State the units).(b) [6 pts] Find the instantaneous rate of change of the number of computers connected to the Internet in 1994. (State the units).S01A Copyright 2001 Department of Mathematics Arizona State University4MAT 210 Test 2 Page 6. The operating cost, C, in thousands of dollars, of a cotton gin plant is given by 39.3857397.23033.0)(2 xxxC where x is the annual quantity of bales in thousands produced. Revenue was estimated at $68.25 per bale.(a) [3 pts] Find the revenue function.(b) [3 pts] Find the profit function.(c) [4 pts] Find the marginal cost when 2500 bales are produced (State the units).(d) [4 pts] Find the marginal revenue when 1600 bales are sold. (State the units)(e) [4 pts] Find the marginal profit when 5800 items are sold. (State the units). S01A Copyright 2001 Department of Mathematics Arizona State