Students can download 11th Business Maths Chapter 5 Differential Calculus Ex 5.3 Questions and Answers, Notes, Samcheer Kalvi 11th Business Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 11th Business Maths Solutions Chapter 5 Differential Calculus Ex 5.3

Samacheer Kalvi 11th Business Maths Differential Calculus Ex 5.3 Text Book Back Questions and Answers

Question 1.
Examine the following functions for continuity at indicated points.
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1
Solution:
(a) f(x) = \(\frac{x^{2}-4}{x-2}\), also given that f(2) = 0
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.1
[∵ x = 2 – h, where h → 0, x → 2]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.2
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.3
∴ The given function is not continuous at x = 2.

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3

(b) Given that f(x) = \(\frac{x^{2}-9}{x-3}\) and f(3) = 6
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.4
[∵ x = 3 – h, where h → 0, x → 3]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.5
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.6
[∵ x = 3 + h, where x → 3, h → 0]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.7
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.8
= 0 + 6
= 6
Also given that f(3) = 6
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q1.9
∴ The given function f(x) is continuous at x = 3.

Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3

Question 2.
Show that f(x) = |x| is continuous at x = 0.
Solution:
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q2
[∵ x = 0 – h]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q2.1
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q2.2
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q2.3
[∵ |x| = x if x > 0]
Samacheer Kalvi 11th Business Maths Guide Chapter 5 Differential Calculus Ex 5.3 Q2.4
∴ f(x) is continuous at x = 0.