PPT - Limits & Continuity - 3 Notes | Study Business Mathematics and Logical Reasoning & Statistics - CA Foundation

 Page 1


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematics 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Page 2


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematics 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
 Continuity  
• Fundamental Knowledge  
• Its application 
2 
Page 3


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematics 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
 Continuity  
• Fundamental Knowledge  
• Its application 
2 
Concept of Continuity 
A function is said to be continuous at a point x = a if 
 (i) f(x) is defined at x = a 
(ii) 
(iii) 
i.e. L.H.L = R.H.L = value of the function at x = a 
3 
Page 4


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematics 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
 Continuity  
• Fundamental Knowledge  
• Its application 
2 
Concept of Continuity 
A function is said to be continuous at a point x = a if 
 (i) f(x) is defined at x = a 
(ii) 
(iii) 
i.e. L.H.L = R.H.L = value of the function at x = a 
3 
Discontinuous Function 
4 
Page 5


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematics 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
 Continuity  
• Fundamental Knowledge  
• Its application 
2 
Concept of Continuity 
A function is said to be continuous at a point x = a if 
 (i) f(x) is defined at x = a 
(ii) 
(iii) 
i.e. L.H.L = R.H.L = value of the function at x = a 
3 
Discontinuous Function 
4 
Properties of Continuous Functions 
(i) If f(x) and g(x) are both continuous at a point x=a, then 
f(x)+g(x) is also continuous. 
(ii) If f(x) and g(x) are both continuous at a point x=a then 
f(x) – g(x) is also continuous. 
(iii) If f(x) and g(x) are both continuous at a point x=a then 
their  product f(x) . g(x) is also continuous at x = a. 
(iv) If f(x) and g(x) are both continuous at a point x=a then 
their quotient f(x)/ g(x)  is also continuous at x=a and 
g(a) ? 0. 
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