Page 40 - Mathematics Class - XII

Table 2: For points on the right of c (= 5):–

x 5.1 5.01 5.001 5.0001 5.00001 5.000001 5.0000001

f (x) 10.1 10.01 10.001 10.0001 10.00001 10.000001 10.0000001

OBSERVATION

1. The value of f (x) is approaching to 10 from the left.

2. The value of f (x) is approaching to 10 from the right.

3. Therefore, lim f (x) = 10 and lim f (x) = 10

x 5 x 5
4. Hence, lim f (x) = 10, f (5) = 10
x→5
Thus, lim f (x) = f (5)

x→5
5. Since, f (5) = lim f (x)
x→5
So the given function is continuous at x = 5

CONCLUSION

From this activity we found the limit of a function f (x) at x = c analytically and checked the function is
continuous.

APPLICATION
This activity is useful in understanding the concept of limit and continuity of a function at a point.

Knowledge Booster
● Every polynomial function is continuous at every point of the real line.
● Every rational function is continuous at every point where its denominator
is different from zero.
● Logarithmic functions, exponential functions, trigonometric functions,
inverse circular functions (inverse trigonometric functions) and modulus
functions are continuous in their respective domains.

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