CH1 Handout Review_page_1
Math 2413 Instructor: Adnan Said Chapter1 Sections 1.2, 1.3, 1.4, and 1.5 1.2 Finding Limits Graphically and Numerically Definition of a…
CH1 Handout Review_page_10
x2-1 4x -4 f(x) is not defined at x = 1. 25) f(x) = ,atx=1 25) (x + 1)(x -1) _ 4(x - 1) Now the function is continuous at x = 1. So, f(x)…
CH1 Handout Review_page_11
30) lim fx)=|5x*2 x<-1 30) x>-1- x-2, x>-l lim f(x} =5(-1) +2=-5+2=-3 x—>-17 1.4 Exercises pg79 (3, 5, 9, 18, 40, 47, 62, 77) (11, 14, 41,…
CH1 Handout Review_page_12
Vertical Asymptote If f(x) approaches infinity (or negative infinit ) as x approaches c from the left or the right, then the line x = c is…
CH1 Handout Review_page_13
36) 37) x2 -2x4+1 x+1 lim x> -17 When x = -1, the denominator is zero and the numerator is not zero. Then x = -1 is a vertical asymptote of…
CH1 Handout Review_page_14
38) lim “2 + x yet 608 2 38) When x = ma the denominator is zero and the numerator is not zero. Then x = 3S is a vertical asymptote of the…
CH1 Handout Review_page_2
Complete the table and use the result to estimate the limit. 3) f(x) = sin = 3) x 2 2 2 2 2 2 x QO |llm |9n | 7m |5n |3n |r f(x) -1 1 |-1 1…
CH1 Handout Review_page_3
6) Find the limit of f(x) as x approaches *. a 3n Sm\3n Tnx ni dot 4Q 4" 49 4 1 1 1 1 lim f(x)=-*» and lim f(x)=~ So, lim f(x) DNE. x> 3n-…
CH1 Handout Review_page_4
Graph the function, and find the indicated limit (if it exists) . 8) f(x) = x-"Find the limit of f(x) as x approaches 1. 8) X- Ifx>1, f(x)…
CH1 Handout Review_page_5
Limit of a Radical Function If f(x) is a radical function, then lim f(x) = f(a) . x>a Evaluate the limit if it exists. 10) lim x2 -19x +25…
CH1 Handout Review_page_6
lim x3 -27 _ 33-27 _0 x73 4x-12 4(3)-12 0 x3 -27 _ (x - 3)(x2 +3x +9) _ x24+3x+9 14) 4x -12 A(x - 3) 4 So, lim x3 -27 _ lim x2+3x+9 _ (3)2…
CH1 Handout Review_page_7
Case 4: If M(a) and N(a) are both zero, convert the complex fraction to a simple fraction , then evaluate the limit. Evaluate the limit if…
CH1 Handout Review_page_8
lim tanx _ 0 20) 20) == x>0O x 0 lim jsinx|| 1 |_ lim |sinx), lim 2 x>O| x cosx} x>0O| x x > 0 |cos x = (1) = 1. 1.3 Exercises pg 67: (25,…
CH1 Handout Review_page_9
Find all points where the function is continuous. 22) f(x) is not continuous at x = 1. 22) 1. f(1) =4, So f(1) is defined. 2. lim f(x)=4,…