Chapter 5.1, Problem 10QR

Evaluate

Evaluate limits x - 3x +2 lim X-1 2x +x-3 lim ii. x9x +1

11. Use the definition of the limit of a function to prove that lim, g(x) =- 6 if x-- 3 if x #- (16х? - 9 4x +3 4 h(x) = 3 if x =- 4

Calculate each limit in Exercises 35. lim -4x-3 36. lim 2x-3/4 37. lim 2r-4/3 38. lim -5x3/5 x00 x-00 39. lim (V – x) 40. lim (r – x³) x00 41. lim (-3x5 + 4x + 11) 42. lim (5 – 2x + 3x³) x00 X-00 x² + 8x + 16 x+1 43. lim x-4 (x+ 4)2(x+ 1) x² +1 44. lim x-+2 (x – 2)2 x+4 45. lim x-0 x(x – 1) 46. lim x-4 x2 + 8x + 16 x - 1 47. lim X0 x - X 48. lim X1 x2 - 2x +1 (3x + 1)²(x – 1) 1- 2r2 49. lim 50. lim x-00 (3 – x) (3 + 4x) X00 1-x3

Evaluate lim [2x] where [x] is the greatest X→0.5 integer function or floor function of x.

Evaluate each expression using the given graph of f(x).Enter DNE if the limit or value does not exist. a) limx→2−f(x)=  b) limx→2+f(x)=  c) limx→2f(x)= d) limx→−2−f(x)= e) limx→−2+f(x)=  f) limx→−2f(x)=  In problems g-i, assume aa is an integer such that −3≤a≤3−3≤a≤3. d) limx→a−f(x)= e) limx→a+f(x)= f) limx→af(x)=