Odd problems

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Question description

Odd problem

f(x) = 3 + x2

(a) (1, 4), (1 + h, 3 + (1 + h)2)

(b) (x, 3 + x2), (x + h, 3 + (x + h)2)

Please also answer the questions attached.

MATH 140 Quiz 2 INSTRUCTIONS • • • • • • NAME:__________________________ The quiz is worth 100 points. There are five problems (each worth 20 points). This quiz is open book and open notes. This means you may refer to your textbook, notes, and online classroom materials. You may take as much time as you wish, provided you turn in your quiz no later than the due date posted in our syllabus. You must show all work in order to receive full credit. If you do not show your work, you may earn only partial or no credit at the discretion of the professor. Emailed quizzes and exams will not be accepted (they crash my email system). Thank you for understanding. If you have any questions, please feel free to email me at: Best of luck! ☺ MULTIPLE CHOICE Select the best answer choice. Write your answer choices below: (1) _____ (2) _____ (3) _____ (4) _____ (5) _____ (1) _____ The first successful ascent to the summit of K2, the world’s second highest and most dangerous mountain was July 31, 1954. The distance (in meters) the climbers ascended K2 is modeled by the graph below. Determine the average rate of ascent from point 𝐴 (“Base Camp”) to point 𝐵 (“Camp IV”). (a) Determine the average rate of ascent from point 𝐴 (“Base Camp”) to point 𝐵 (“Camp IV”). (b) Estimate the instantaneous velocity of ascent of the climbers at Camp IV. 𝐵 6000 Distance (𝑚) 1000 𝐴 1 4 𝑥 Time (𝑤𝑒𝑒𝑘𝑠) (𝐴) 1666.7 𝑚⁄𝑤𝑒𝑒𝑘 (𝐵) 1245.5 𝑚⁄𝑤𝑒𝑒𝑘 (𝐶) 612.2 𝑚⁄𝑤𝑒𝑒𝑘 (𝐷) 166.7 𝑚⁄𝑤𝑒𝑒𝑘 (𝐸) 𝑛𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 (2) _____ Consider the following function 3𝑥 + 2 𝑔(𝑥) = { 3 𝑥≠2 𝑥=2 How close to 𝑐 = 2 must 𝑥 be in order for 𝑔(𝑥) to differ from 8 by less than 0.001? (𝐴) 0.0001 (𝐵) 0.0002 (𝐶) 0.0003 (𝐷) 0.0004 (𝐸) 𝑛𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 (3) _____ Find an equation of the tangent line to the curve 𝑦 = 1⁄𝑥 at the point 𝐴(2, 1⁄2). (𝐴) 𝑦 = 1 1 𝑥− 2 2 1 (𝐵) 𝑦 = − 𝑥 + 1 4 1 3 (𝐶) 𝑦 = − 𝑥 − 4 2 1 (𝐷) 𝑦 = 𝑥 4 (𝐸) 𝑛𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒 (4) _____ Find the following limit, provided it exists (Note: You must use the correct approach to receive credit.) 1 lim 𝑥 2 cos ( ) 𝑥→0 𝑥 (5) _____ Suppose 𝑦 = √𝑥. Where is the slope of the tangent line equal to 1⁄6? (𝐴) 1⁄6 (𝐵) √1⁄6 (𝐶) 3 (𝐷) 9 (𝐸) 𝑛𝑜𝑛𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑎𝑏𝑜𝑣𝑒

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