Ex 5.1

Chapter 5 Class 12 Continuity and Differentiability
Serial order wise

### Transcript

Ex 5.1, 3 Examine the following functions for continuity. (c) f (x) = (π₯^(2 )β 25 )/(π₯ + 5), x β  β5 f (x) = (π₯^(2 )β 25 )/(π₯ + 5) Putting x = β5 f (β5) = (γ(β5)γ^(2 )β 25 )/(β5 + 5) = (25β 25 )/(β5 + 5) = 0/0 = Undefined Hence, f(x) is not defined at x = β5 So, we check for continuity at all points except β5 Let c be any real number except β5. f is continuous at π₯ = π if (π₯π’π¦)β¬(π±βπ) π(π) = π(π) LHS (π₯π’π¦)β¬(π±βπ) π(π) = limβ¬(xβπ) (π₯^2β 25)/(π₯ + 5) = limβ¬(xβπ) ((π₯ β 5) (π₯ + 5))/(π₯ + 5) = limβ¬(xβπ) π₯β5 Putting x = c = c β 5 RHS f (c) = (π^(2 )β 25 )/(π + 5) = ((π β 5)(π + 5))/((π + 5)) = c β 5 Let c be any real number except β5. f is continuous at π₯ = π if (π₯π’π¦)β¬(π±βπ) π(π) = π(π) Since, L.H.S = R.H.S β΄ Function is continuous at x = c (except β5) Thus, we can write that f is continuous for all real numbers except β5 β΄ f is continuous at each π± β R β {βπ}

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.