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


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


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Limits    
• Fundamental Knowledge  
• Its application 
2 
Concept of Limit 
 x tends to zero or x ? 0    
x tends to a finite quantity or x ? b  
x tends to a infinity or x ? 8  
3 
Page 4


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Limits    
• Fundamental Knowledge  
• Its application 
2 
Concept of Limit 
 x tends to zero or x ? 0    
x tends to a finite quantity or x ? b  
x tends to a infinity or x ? 8  
3 
Meaning of x tends to zero 
Suppose that the maid of Neeta has to pay a debt of Rs. 
104 to Neeta. She pays 50% of a debt every month, when 
she will be able to repay the whole amount of debt.  
 
Solution: 
Let x be the debt at the end of the any month.  
At the end of 1
st
 month, x = Rs. 52 
At the end of 2
nd
 month, x = Rs. 26 
At the end of 3
rd
 month, x = Rs. 13 
 
 
4 
Page 5


Limits and Continuity – Intutive Approach–  
Chapter 8 
Paper 4: Quantitative Aptitude- Mathematices 
Ms. Ritu Gupta B.A. (Hons.) Maths and MA (Maths) 
 
 
 
 
 
Limits    
• Fundamental Knowledge  
• Its application 
2 
Concept of Limit 
 x tends to zero or x ? 0    
x tends to a finite quantity or x ? b  
x tends to a infinity or x ? 8  
3 
Meaning of x tends to zero 
Suppose that the maid of Neeta has to pay a debt of Rs. 
104 to Neeta. She pays 50% of a debt every month, when 
she will be able to repay the whole amount of debt.  
 
Solution: 
Let x be the debt at the end of the any month.  
At the end of 1
st
 month, x = Rs. 52 
At the end of 2
nd
 month, x = Rs. 26 
At the end of 3
rd
 month, x = Rs. 13 
 
 
4 
Meaning of x tends to zero – Continued  
5 
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FAQs on PPT - Limits & Continuity - 2 - Quantitative Aptitude for CA Foundation

1. What are limits in calculus?
Ans. Limits in calculus are used to describe the behavior of a function as it approaches a certain value or as the input values get arbitrarily close to a particular point. It helps determine the values that a function approaches or that it does not approach as the input approaches a given value.
2. How do you find limits algebraically?
Ans. To find limits algebraically, you can use various techniques such as factoring, rationalizing the numerator or denominator, and applying algebraic manipulations. You can also use special limit rules, such as the limit laws, to simplify the expression and evaluate the limit.
3. What is continuity in calculus?
Ans. Continuity in calculus refers to the property of a function where there are no sudden jumps, holes, or breaks in the graph. It means that the function is defined at every point in its domain and there are no abrupt changes in its behavior. A function is continuous if it can be drawn without lifting the pen from the paper.
4. How do you determine if a function is continuous?
Ans. A function is continuous if three conditions are met: 1) the function is defined at the point in question, 2) the limit of the function exists at that point, and 3) the value of the function at that point is equal to the limit. If any of these conditions fail, then the function is not continuous at that point.
5. What are the different types of discontinuities?
Ans. There are three main types of discontinuities: 1) Removable discontinuity, where there is a hole in the graph that can be filled to make the function continuous, 2) Jump discontinuity, where there is a sudden jump or gap in the graph, and 3) Infinite discontinuity, where the function approaches positive or negative infinity at a certain point.
147 videos|175 docs|99 tests
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