Page 245 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes
1. If find whether the function f is continuous at x = 2.

2. Determine whether f(x) is continuous at x = 2, where

3. Examine the continuity of f(x) at x = 1, where

4. Determine the values of k so that the function

is continuous at x = 2.

Example
A travel agency charges Rs 10 per km for travelling upto 300 kms. The agency gives a discount
of Rs 2 per km, in revenue, for distance covered in excess of 300 kms. Express the revenue of
the company as a function of the distance covered and examine its continuity when distance
travelled is 300 kms.

Solution:
Let be the distance covered in kms and ( ) be the revenue.

R(x) =

R(x) =

Now R(300) = 10 × 300 = 3000
LHL = 10 × 300 = 3000
RHL = 8 × 300 + 600 = 3000
Since LHL = RHL = R(300)
The function is continuous at x = 300.

Example

A wholesaler of pencils charges 30 per dozen on orders of 50 dozens or less. For orders in excess
of 50 dozens, the price charged is 29. If denote the no. of dozens of pencils, express the revenue
function of the wholesaler as a function of . Is this function continuous everywhere?

Solution:
We can write the revenue function as

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