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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. 
5 
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FAQs on PPT - Limits & Continuity - 3 - Quantitative Aptitude for CA Foundation

1. What is the definition of a limit in calculus?
Ans. In calculus, a limit is a fundamental concept that describes the behavior of a function as the input value approaches a certain value. It determines the value that a function 'approaches' as the input gets closer and closer to a specific point.
2. How do you find the limit of a function algebraically?
Ans. To find the limit of a function algebraically, you can use various techniques such as factoring, rationalizing, or applying algebraic manipulations to simplify the expression. Once the expression is simplified, you can substitute the desired value into the expression to evaluate the limit.
3. What is the difference between a removable and non-removable discontinuity?
Ans. A removable discontinuity, also known as a removable singularity, occurs when a function has a hole in its graph at a specific point but can be filled by redefining the function at that point. On the other hand, a non-removable discontinuity, also known as an essential singularity, is a point where the function cannot be redefined to fill the gap in its graph.
4. How can you determine if a function is continuous at a specific point?
Ans. To determine if a function is continuous at a specific point, you need to check three conditions: 1) The function must be defined at that point, 2) The limit of the function as the input approaches that point must exist, and 3) The limit value must be equal to the function value at that point. If all these conditions are satisfied, the function is continuous at that point.
5. What is the Intermediate Value Theorem and how is it used?
Ans. The Intermediate Value Theorem states that if a continuous function takes on two different values at two points in its domain, then it must also take on every value between those two points. This theorem is commonly used to prove the existence of solutions or roots to equations, as it guarantees that a continuous function will cross the x-axis at least once between two points where the function values have opposite signs.
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