# ESTIMATING LIMIT VALUE FROM GRAPHS

## About "Estimating Limit Values From Graphs"

Estimating Limit Values From Graphs :

Here we are going to see how to estimate limits from graph.

## Required Condition for Existence of Limit of Function

lim x->x0 f(x)  =  L exists if the following hold :

(i) lim x->x0+ f(x) exists,

(ii)  lim x->x0- f(x) exists, and

(iii)  lim x->x0+ f(x)  =   lim x->x0- f(x)  =  L

Question 1 :

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?

lim x->1  sin πx

Solution :

When 1 approaches from left hand side, we get the value closer to 0.

When 1 approaches from right hand side, we get the value closer to 0.

Hence the required limit 0.

Question 2 :

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?

lim x->1  sec x

Solution :

When 1 approaches from left hand side, we get the value closer to 1.

When 1 approaches from right hand side, we get the value closer to 1.

Hence the required limit 1.

Question 3 :

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?

lim x->π/2 tan x

Solution :

When 1 approaches from left hand side, we get the value closer to 1.

When 1 approaches from right hand side, we get the value closer to 1.

Hence the function does not exist.

Question 4 :

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?

lim x->1 f(x)

Where f(x)  =  x2 + 2      x ≠ 1

=    1            x = 1

Solution :

To find the value of left hand limit and right hand limit for x -> 1, we have to use the function f(x)  =  (x2 + 2). It is enough to check if we get equal values for left hand and right hand limit.

 f(x)  =  (x2 + 2)lim x->1- f(x)  =  12 + 2  =  3 f(x)  =  (x2 + 2)lim x->1+ f(x)  =  12 + 2  =  3

lim x->1- f(x)  =  lim x->1+ f(x)

Hence the required limit is 3.

Question 5 :

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?

lim x->3 1/(x- 3)

Solution :

From the graph given above, we get different values for left hand limit and right hand limit.

The function does not exist at x - >3.

Question 6 :

Use the graph to find the limits (if it exists). If the limit does not exist, explain why?

lim x->5 |x - 5|/(x - 5)

Solution :

From the graph given above, we get different values for left hand limit and right hand limit.

The function does not exist at x - >5.

After having gone through the stuff given above, we hope that the students would have understood, "Estimating Limit Values From Graphs"

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