In Each Part Sketch a Continuous Curve Y F X With the Stated Properties F 2 4 F 2 0
HOW TO SKETCH A GRAPH OF A FUNCTION WITH LIMITS
About "How to Sketch a Graph of a Function With Limits"
How to Sketch a Graph of a Function With Limits :
Here we are going to see how to sketch a graph of a function with limits.
Question 1 :
Sketch the graph of a function f that satisfies the given values :
f(0) is undefined
lim x -> 0 f(x) = 4
f(2) = 6
lim x -> 2 f(x) = 3
Solution :
From the given question,
- We understood that the functions is undefined when x = 0.
- When the value of x approaches 0 from left hand side and right hand side, limit value will approaches to 4.
- When x = 2, the value of y will be 6.
- When the value of x approaches 2 from left hand side and right hand side, limit value will approaches to 3.
The value of x approaches from left and right, the limit will approach the value 4.
When x approaches 2 from left and right, the limit will approaches to 3. The picture given above will illustrate the condition.
When x = 2, f(x) that is the value of y will be 6.
Hence the picture given above is the required graph of the statements given.
Question 2 :
Sketch the graph of a function f that satisfies the given values :
f(-2) = 0
f(2) = 0
lim x -> -2 f(x) = 0
lim x -> 2 f(x) does not exists
Solution :
From the given question,
When x = -2, the value of y will be 0.
When x = 2, the value of y will be 0.
When x tends to 2, the function does not exist. To show this, we have to show the graph with different values of y.
Question 3 :
Write a brief description of the meaning of the notation lim x -> 8 f(x) = 25
Solution :
When x approaches from left side and right side, the value of limit will approaches 25.
| lim x -> 8- f(x) = 25 | lim x -> 8+ f(x) = 25 |
Question 4 :
If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?
Solution :
The given statement represents, when x = 2, the value of y will be 4.
Case 1 :
When x approaches from left side and right side, we will get same values approximately, or
Case 2 :
When x approaches from left side and right side, we will get different values.
Hence, we cannot conclude anything about the limit of f(x) as x approaches 2?
Question 5 :
If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain reasoning.
Solution :
Given :
lim x -> 2 f(x) = 4
From this, we may understand that
| lim x -> 2- f(x) = 4 | lim x -> 2+ f(x) = 4 |
when x approaches 2 from left side and right side, the limit will approaches to 4.
Hence we cannot conclude anything about f(2).
Question 6 :
Evaluate :
lim x->3 (x2 -9)/(x - 3) if it exists by finding f(3+) and f(3-)
Solution :
= im x->3 (x2 -9)/(x - 3)
= im x->3 (x + 3)(x - 3)/(x - 3)
= im x->3 (x + 3)
| im x->3+ f(x) = 3 + 3 = 6 | im x->3-f(x) = 3 + 3 = 6 |
Question 7 :
Verify the existence of lim x -> 1 f(x)
Solution :
If the limit x -> 1 exists, then
lim x-> 1- f(x) = lim x-> 1+ f(x)
| f(x) = (x - 1)/(x - 1) f(x) = 1 lim x-> 1 + f(x) = 1 | f(x) = -(x - 1)/(x - 1) f(x) = -1 lim x-> 1 - f(x) = -1 |
Since lim x-> 1 - f(x) ≠ lim x-> 1 + f(x), the limit does not exists.
After having gone through the stuff given above, we hope that the students would have understood, " How to Sketch a Graph of a Function With Limits"
Apart from the stuff given in " How to Sketch a Graph of a Function With Limits" , if you need any other stuff in math, please use our google custom search here.
Kindly mail your feedback tov4formath@gmail.com
We always appreciate your feedback.
© All rights reserved. onlinemath4all.com
Source: https://www.onlinemath4all.com/how-to-sketch-a-graph-of-a-function-with-limits.html
0 Response to "In Each Part Sketch a Continuous Curve Y F X With the Stated Properties F 2 4 F 2 0"
Post a Comment