Let f(x) = (1 +x)1/X. (a) Estimate the value of the limit lim0 (1 + X)1 /X to ve decimal places. Does this number look familiar? x_. :] (b) Illustrate part (a) by graphing the function y = (1 + x)1/X. y y y 1 1 1 1 S . . . . ._. . . . . ..i . ._. . . . . . x . ._i . . . ._. . 11 ._._ x 15 10 10 5 5 10 15 15 10 5 10 15 5 5 10 10 15 15 1. [-/6 Points] DETAILS SCALCCCH4 2.3.001. MY NOTES PRACTICE ANOTHER 2. [-/6 Points] DETAILS SCALCCCH4 2.3.002. MY NOTES Given that The graphs of fand g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.) lim f(x) = 4 lim g(x) = -2 lim h ( x ) = 0 , x - 2 x - 2 find the limits, if they exist. (If an answer does not exist, enter DNE.) y = f(x) y = g(x) lim [f(x) + 5g(x)] (b) lim [g(x)]3 (a) lim [f(x) + g(x)] (c) lim VA( x ) X-2 (b) lim [f(x) + 9(x)] x- 1 (d) lim 3R(x) x- 2 9(x) (c) lim [f(x)g(x)] x -0 (e) lim x) x- 2 h(x) (d) lim x) X- -1 9(x) f) lim 9(x)h(x) x - 2 {(x) e) lim [x3{(x)] lim v 3 + f(x) 3. [-/1 Points] DETAILS SCALCCCH4 2.3.003. MY NOTES PRACTICE ANOTHER Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim (3x4 + 2x2 - x+ 1) * - -14. [-/1 Points] DETAILS SCALCCCH4 2.3.005. MY NOTES PRACTICE ANOTHER 7. [-/1 Points] DETAILS SCALCCCH4 2.3.009. MY NOTES PRACTICE ANOTHER Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim (1 + Vx ) ( 4 - 5x2 + * 3 ) lim x - 5x + 4 x - x - 4 Need Help? Watch It 8. [-/1 Points] DETAILS SCALCCCH4 2.3.011. MY NOTES PRACTICE ANOTHER 5. [-/1 Points] DETAILS SCALCCCH4 2.3.007. MY NOTES PRACTICE ANOTHER Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim X- - 4x + 3 x - 5 x - 5 Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim 3x + 4 3 x - 2 9. [-/1 Points] DETAILS SCALCCCH4 2.3.013. MY NOTES PRACTICE ANOTHER Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 6. [-/2 Points] DETAILS SCALCCCH4 2.3.008. MY NOTES PRACTICE ANOTHER lim 2 - 16 1- -4 21 + 9t + 4 (a) What is wrong with the following equation? * + x - 6 = x+ 3 x - 2 Need Help? Watch It O ( x - 2) ( x + 3) # x+ x - 6 O The left-hand side is not defined for x = 0, but the right-hand side is. The left-hand side is not defined for x = 2, but the right-hand side is. 10. [-/1 Points] DETAILS SCALCCCH4 2.3.015. MY NOTES PRACTICE ANOTHER None of these - the equation is correct. Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) (b) In view of part (a), explain why the equation lim (1 + h)2 - 1 lim x+ x -6 = lim (x+3) h - 0 h x - 2 X- 2 X - is correct. O Since + X-6 and x + 3 are both continuous, the equation follows. x - 2 Need Help? Watch It Since the equation holds for all x # 2, it follows that both sides of the equation approach the same limit as x - 2. This equation follows from the fact that the equation in part (a) is correct. O None of these - the equation is not correct