# Calculus Home work Due Monday 16, XXXXXXXXXXLet f(x) = 3x2 - 5x + 2. Evaluate limx?-2 f(x). 2. Calculate limx?2 x2-4 x XXXXXXXXXXCalculate limt?1 5t2+6t+1 8t XXXXXXXXXXCalculate limx?3vx XXXXXXXXXX 5....

Calculus Home work Due Monday 16, XXXXXXXXXXLet f(x) = 3x2 - 5x + 2. Evaluate limx?-2 f(x). 2. Calculate limx?2 x2-4 x XXXXXXXXXXCalculate limt?1 5t2+6t+1 8t XXXXXXXXXXCalculate limx?3vx XXXXXXXXXX
5. Let f(x) = 3b v4b+1-1. Find limb?2 f(b) and limb?0 f(b). The first limit is very easy, the second requires some manipulation on your part.
6. (One-sided limits)
Let f(x) =
0 if x = 2 v25 - x2 if 2
Compute the following limits (a) limx?5- f(x), (b)limx?5+ f(x), (c)limx?5 f(x) ,limx?2- f(x), (d)limx?2+ f(x), (e)limx?2 f(x), (f) limx?100 f(x) 7. Calculate limh?0 v16+h-4 h 8.Assume limx?3 g(x) and f(x) = g(x) whenever x =? 3. What is limx?3 f(x)? Explain your answer.
Note that all these problems are from Section 2.3. Pleasee work out as many as you can from this section. I can put too many problems on the homework–I expect you to workout as many problems as you can from the Book.
1
Document Preview:

Calculus Home work Due Monday 16, 201321. Let f(x) = 3x 5x + 2. Evaluate lim f(x).x!22x42. Calculate lim .x!2x225t +6t+13. Calculate lim .t!18t4p324. Calculate lim x 10.x!33bp5. Let f(x) = . Find lim f(b) and lim f(b). The rst limit is very easy,b!2 b!04b+11the second requires some manipulation on your part.6. (One-sided limits)8>0 if x 2<><>:3x if x 5Compute the following limits (a) lim f(x), (b)lim +f(x), (c)lim f(x) ,lim f(x),x!5 x!5 x!5 x!2+(d)lim f(x), (e)lim f(x), (f) lim f(x)x!2 x!2 x!100p16+h47. Calculate limh!0h8.Assume lim g(x) and f(x) = g(x) whenever x =6 3. What is lim f(x)? Explainx!3 x!3your answer.Note that all these problems are from Section 2.3. Pleasee work out as many as you canfrom this section. I can put too many problems on the homework{I expect you to workoutas many problems as you can from the Book.1

## Solution

Robert answered on Dec 31 2021
Sol: (1)   23 5 2f x x x  
   
   
 
2
2 2
2
2
lim lim 3 5 2
3 2 5 2 2
12 10 2
lim 24
x x
x
f x x x
f x
 

  
    
  

Sol: (2)
   
 
 
2
2 2
2
2
2
2 24
lim lim
2 2
lim 2
2 2
4
lim 4
2
x x
x
x
x xx
x x
x
x
x
 

 

 
 
 

Sol: (3)
   
 
22
1
2
1
5 1 6 1 15 6 1
lim
8 4 8 1 4
5 6 1
8 4
12
4
5 6 1
lim 3
8 4
t
t
t t
t
t t
t

  

 
 

 

Sol: (4)
 
223 3
3
3
3
3
23
3
lim 10 3 10
9 10
1
1 3
lim 10
2 2
x
i
x
x
e
i
x

  
 
 

  
Sol: (5)  
3
4 1 1
f x

 

(a)
 
 
 
 
2 2
2
3
lim lim
4 1 1
3 2
4 2 1 1
6
8 1 1
6
9...
SOLUTION.PDF