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 f and 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 , find the limits, if they exist. (If an answer does not exist, enter DNE.) y = f(x) = g(x) (a) lim [f(x) + 5g(x)] (b) lim, [8(x)]3 lim, (fix) + 8(x)] () lim v f(x) lim Vox) + 8(x)] d) lim 3(x) x - 2 8 ( x ) lim voxg (x)] lim 8( d) lim Ax 1 lim 86xh(x ) e ) lim (x 3 full (f lim v3 + 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 + 2x 2 - x + 1 ) .- - -........ 4. [-/1 Points] DETAILS SCALCCCH4 2.3.005. MY NOTES PRACTICE ANOTHER Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim (1 + Vx ) ( 4 - 5 x 2 + * 3 ) Need Help? Watch It. [-/1 Points] DETAILS SCALCCCH4 2.3.007. MY NOTES PRACTICE ANOTHER 9. [-/1 Points] DETAILS SCALCCCH4 2.3.013. 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.) 3x2 + 4 12 - 16 2 V 3x - 2 lim - - -4 2t2 + 9t + 4 Need Help? Watch It 6. [-/2 Points] DETAILS SCALCCCH4 2.3.008. MY NOTES PRACTICE ANOTHER (a) What is wrong with the following equation? 10. [-/1 Points] DETAILS SCALCCCH4 2.3.015. MY NOTES PRACTICE ANOTHER x2 + x - 6 =x+3 x - 2 O ( x - 2)(x+ 3)# x2 + x- 6 Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) The left-hand side is not defined for x = 0, but the right-hand side is. lim (1 + h)2 - 1 h - 0 The left-hand side is not defined for x = 2, but the right-hand side is. None of these - the equation is correct. Need Help? Watch It (b) In view of part (a), explain why the equation lim X4 + x - 6 = 1 2x- 2 x-2 11. [-/1 Points] DETAILS SCALCCCH4 2.3.017. MY NOTES PRACTICE ANOTHER is correct. Since * + X - and x + 3 are both continuous, the equation follows. x - 2 Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) Since the equation holds for all x # 2, it follows that both sides of the equation approach the same limit as x -> 2. lim *+ 4 x - -4 x3+64 This equation follows from the fact that the equation in part (a) is correct. None of these - the equation is not correct. Need Help? Watch It 7. [-/1 Points] DETAILS SCALCCCH4 2.3.009. MY NOTES PRACTICE ANOTHER 12. [-/1 Points] DETAILS SCALCCCH4 2.3.019. MY NOTES PRACTICE ANOTHER Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim X2 - 5x + 4 Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x -+ 4 x - 4 1+1 - -2 2 +X 8. [-/1 Points] DETAILS SCALCCCH4 2.3.011. MY NOTES PRACTICE ANOTHER Need Help? Watch It Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) lim x 2 - 4x + 3 x - 5 x - 5 13. [-/1 Points] DETAILS SCALCCCH4 2.3.021. MY NOTES PRACTICE ANOTHER Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 6- Vx X - 36 36X - x2 Need Help? Watch It14. [-/1 Points] DETAILS SCALCCCH4 2.3.023. MY NOTES PRACTICE ANOTHER 19. [-/7 Points] DETAILS SCALCCCH4 2.3.037. MY NOTES PRACTICE ANOTHER Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) Let if x 2 (a) Evaluate each of the following, if it exists. (If an answer does not exist, enter DNE.) 15. [-/6 Points] DETAILS SCALCCCH4 2.3.027. MY NOTES PRACTICE ANOTHER lim 8(x) X - 1 - Use the Squeeze Theorem to show that lim (x2 cos 207rx) = 0. Illustrate by graphing the functions f(x) = -x2, g(x) = x2 cos 207tx, and h(x) = x2 on the same ii) lim g(x) screen. Let f(x) = -x2, g(x) = x2 cos 207tx, and h(x) = x2. Then ? @ scos 20xxs ? @ => ? @ sx2 cos 20xxs ? . Since im fix) = lim h(x) = by the Squeeze Theorem we have lim g(x) = (ii) 8(1) Need Help? Watch It (v) lim g(x X -2- 16. [-/1 Points] DETAILS SCALCCCH4 2.3.029. MY NOTES PRACTICE ANOTHER v) lim g(x ) If 3x - 5 s f(X) sx2 - 3x + 4 for x 20, find lim f(x) (vi) lim 8 ( x ) Need Help? Watch It (b) Sketch the graph of g. g(x) g(X) 17. [-/1 Points] DETAILS SCALCCCH4 2.3.033. MY NOTES PRACTICE ANOTHER Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim (8x + [x - 71) -5 -5 -5 O O Need Help? Watch It g(x) 8(x) 18. [-/1 Points] DETAILS SCALCCCH4 2.3.035. MY NOTES PRACTICE ANOTHER Find the limit, if it exists. (If an answer does not exist, enter DNE.) - X lim (x- -5