MATH 1505 Study Guide - Quiz Guide: 32X, Mean Value Theorem, Ferris Wheel

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mauvearmadillo869

7 Dec 2018

School

York University

Department

Mathematics and Statistics

Course

MATH 1505

Professor

Norman Purzitsky

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Document Summary

Show all your work: find the limit. Solution: let y = (ex + x) (ex + x) 1 x : ln y = 1 x ln (ex + x) lim x!1 ln y = lim x!1 ln (ex + x) x (note: this is in the form 1. 1 ex + 1 (note: this is in the form 1 ex + x. 1 (note: this is in the form 1. 1 ex ex + 1 ex ex = 1: lim x!1 y = lim x!1 eln y = e: (cid:3) 2x + 5(cid:19)2x+1 x!1(cid:18) 2x (cid:0) 3 ln(cid:18) 2x (cid:0) 3. 2x + 5(cid:19) (2x + 1) ln(cid:18) 2x (cid:0) 3 ln(cid:0) 2x(cid:0)3. 8 (2x + 1)2 (2x (cid:0) 3) (2x + 5) Therefore, lim x!1 y = lim x!1 eln y = e(cid:0)8: (cid:3: page 247, #40. A ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes.

Related Questions

4. (21 pts) Let g be the function given by ( 6 - X 2 + x if x < 2, x + -2 g(x) = x2 – x-1 if x>2. (a) (6 pts) Use the definition of continuity to determine whether the function g is continuous at 2. Show your work. (b) (3 pts) Evaluate the limit. Justify your answer. Show your work. Write "does not exist" only if the limit does not exist and is not + or -0. lim g(x) = lim -2+ = +00 X 2 + X since the form of the limit is NUM: POS, DENOM: POS (c) (2 pts) Write the equation(s) of all vertical asymptotes of g. Write "none" if appropriate. The result in part (b) implies that the line x= -2 is a vertical asymptote. This is the only vertical asymptote, since the function g is continuous on its domain (d) (2 pts) Determine the largest) intervals of continuity of g. Use interval notation to write your answer. Let g be the function given by 12+ if x < 2, x# -2 2 + x g(x)= x2-x-1 x-1 if x>2. (e) (6 pts) Evaluate each limit. Do not use L'Hôpital's Rule. Write "does not exist" only if the limit does not exist and is not too or -00. Show your work. 6-1 i lim g(x) = lim -00 2 + X = lim -002 + x 0-1 + 1 x -00 x x x -+- 2 +1 0 0 + 11 x2 - x-1 1 ii. lim g(x) = lim x++ V x2 – x-1 X-1 x2 - x-1 X - 1 = lim x +oc x +0 - lim Vam M93001 (f) (2 pts) Write the equation(s) of all horizontal asymptotes of g. Write "none" if appropriate.