RD Sharma Class 11 Solutions Chapter 29 - Limits (Ex 29.10) Exercise 29.10

Class 11 Chapter 29 - Limits (Ex 29.10) RD Sharma Solutions Free PDF

A limit is a value a function approaches as any value is reached by the input. For calculus and mathematical analysis, limits are important and are used to define continuity, derivatives, and integrals.

It is the basis for calculus and supports the topic in higher classes.

RD Sharma Class 11 Solutions Chapter 29 - Limits (Ex 29.10) Exercise 29.10 - Free PDF has been compiled by the experts at Vedantu aimed at making the preparation of students more effective and helping them to secure more marks in the exams.

List of Exercises in RD Sharma Class 11 Solutions Chapter 29 - Limits -

Chapter 29 of RD Sharma Class 11 contains 11 exercises and each exercise has 5 questions. Solutions of all the exercises are compiled and made available on the website and mobile application of Vedantu.

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Concept Clarity - The solutions provided are simplified for the better understanding of the students
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FAQs on RD Sharma Class 11 Solutions Chapter 29 - Limits (Ex 29.10) Exercise 29.10

1. What is the primary method for solving problems in RD Sharma Class 11 Solutions for Chapter 29, Exercise 29.10?

The primary method for solving problems in this exercise involves evaluating limits that result in the indeterminate form 1^∞. The step-by-step process is as follows:

First, verify that direct substitution leads to the 1^∞ form.
Next, manipulate the expression to fit the standard structure: lim [1 + f(x)]^g(x), where f(x) → 0.
Apply the standard formula: The limit equals e^{lim [f(x) * g(x)]}.
Finally, solve the simpler limit in the exponent to get the final answer.

This technique is consistently applied across all questions in Exercise 29.10.

2. How do you correctly identify and set up the function f(x) when the limit is not in the standard (1+x) form?

To correctly set up the function, you must algebraically transform the base to be in the form '1 + f(x)'. For an expression like (a+x)/(b+x), you would rewrite it as 1 + [(a+x)/(b+x) - 1], which simplifies to 1 + (a-b)/(b+x). Here, f(x) is (a-b)/(b+x). The key is to add and subtract 1 from the base of the function to isolate the '1' and correctly identify the f(x) term that approaches zero.

3. Why does the formula for the 1^∞ indeterminate form involve the constant 'e'?

The use of 'e' stems from its fundamental definition as a limit: e = lim (1 + 1/n)ⁿ as n → ∞. The problems in Exercise 29.10 are variations of this fundamental limit. By using logarithms and limit properties, any function of the form [f(x)]^g(x) that approaches 1^∞ can be transformed into an expression whose limit is a power of 'e'. This makes 'e' the natural base for resolving this specific type of indeterminate form.

4. What is a common mistake students make when evaluating limits in RD Sharma Exercise 29.10?

A common mistake is incorrectly calculating the limit of the exponent after applying the formula. Students often correctly transform the limit into the e^{lim [f(x) * g(x)]} form but then make an error while simplifying the product f(x) * g(x). It is crucial to carefully apply algebraic simplification, factorization, or other limit rules to evaluate the exponent's limit before stating the final answer as a power of 'e'.

5. How does solving a limit in Exercise 29.10 differ from using L'Hôpital's Rule?

The standard method for Exercise 29.10 uses a direct formula for the 1^∞ form. L'Hôpital's Rule is an alternative, more general method. To use it, you would first take the natural logarithm of the function, which converts the 1^∞ form into a 0/0 or ∞/∞ form. You can then apply L'Hôpital's Rule to the resulting expression. Finally, you must remember to exponentiate the result to find the original limit. The formulaic method is often faster if you remember it, while L'Hôpital's Rule is a powerful alternative if you forget the specific formula.

6. Are the methods in RD Sharma for limits aligned with the Class 11 CBSE syllabus for 2025-26?

Yes, the methods for evaluating limits presented in RD Sharma Chapter 29, including the evaluation of exponential and logarithmic limits (like the 1^∞ form), are fully aligned with the CBSE Class 11 Maths syllabus for 2025-26. Mastering these techniques is essential for understanding the 'Limits and Derivatives' unit, which is a foundational topic for calculus in both Class 11 and Class 12.