- #1
nycmathguy
- Homework Statement
- Use tables to determine a limit.
- Relevant Equations
- Linear Equation
:: Tables and Limits
Complete a table for f(x) = x + 3 as x→2 from the right and left.
As x tends to 2 from the left side, the given values for x are: 1.9, 1.99, 1.999.
As x tends to 2 from the right side, the given values for x are: 2.001, 2.01, 2.1.
Let me see if I can do this.
I think this question is just an evaluation exercise. I got to plug all the given x-values to evaluate f(x) as x tends to 2.
Each value of x from the left and right gets closer and closer to 2 but f(x) never reaches 2. By this I mean f(x) gets extremely close to 2 but never becomes 2. Is this not the basic limit idea as taught in first semester calculus?
Moving on. This reply is going to drag. How do you think I feel using my cell phone to type all this work?
Our function f(x) = x + 3 is a line.
As x tends to 2 from the left side, the given values for x are: 1.9, 1.99, 1.999.
f(x) = x + 3
f(1.9) = 1.9 + 3 = 4.9
f(1.99) = 1.99 + 3 = 4.99
f(1.999) = 1.999 + 3 = 4.999
Rounding to the units place, I get 5.
The limit is 5.
Yes?
As x tends to 2 from the right side, the given values for x are: 2.001, 2.01, 2.1.
f(x) = x + 3
f(2.001) = 2.001 + 3 = 5.001
f(2.01) = 2.01 + 3 = 5.01
f(2.1) = 2.1 + 3 = 5.1
Rounding to the units place, I get 5.
I conclude the limit is 5.
All of this tells me that the LHL = RHS = 5.
The limit of f(x) as x-->2 is 5.
You say?
Now to make a table.
For the table as x-->2 from the left side:
x: 1.9... . .1.99...1.999
f(x): 4.9. 4.99. 4.999
For the table as x-->2 from the right side:
x: 2.001...2.01...2.1
f(x): 5.001...5.01...5.1
Trust me, I don't plan to do another "complete a table" problem for a very long time. Is any of this right?
Complete a table for f(x) = x + 3 as x→2 from the right and left.
As x tends to 2 from the left side, the given values for x are: 1.9, 1.99, 1.999.
As x tends to 2 from the right side, the given values for x are: 2.001, 2.01, 2.1.
Let me see if I can do this.
I think this question is just an evaluation exercise. I got to plug all the given x-values to evaluate f(x) as x tends to 2.
Each value of x from the left and right gets closer and closer to 2 but f(x) never reaches 2. By this I mean f(x) gets extremely close to 2 but never becomes 2. Is this not the basic limit idea as taught in first semester calculus?
Moving on. This reply is going to drag. How do you think I feel using my cell phone to type all this work?
Our function f(x) = x + 3 is a line.
As x tends to 2 from the left side, the given values for x are: 1.9, 1.99, 1.999.
f(x) = x + 3
f(1.9) = 1.9 + 3 = 4.9
f(1.99) = 1.99 + 3 = 4.99
f(1.999) = 1.999 + 3 = 4.999
Rounding to the units place, I get 5.
The limit is 5.
Yes?
As x tends to 2 from the right side, the given values for x are: 2.001, 2.01, 2.1.
f(x) = x + 3
f(2.001) = 2.001 + 3 = 5.001
f(2.01) = 2.01 + 3 = 5.01
f(2.1) = 2.1 + 3 = 5.1
Rounding to the units place, I get 5.
I conclude the limit is 5.
All of this tells me that the LHL = RHS = 5.
The limit of f(x) as x-->2 is 5.
You say?
Now to make a table.
For the table as x-->2 from the left side:
x: 1.9... . .1.99...1.999
f(x): 4.9. 4.99. 4.999
For the table as x-->2 from the right side:
x: 2.001...2.01...2.1
f(x): 5.001...5.01...5.1
Trust me, I don't plan to do another "complete a table" problem for a very long time. Is any of this right?