Table of Contents
Subject specialists have created NCERT Exemplar Solutions for Class 11 Maths Chapter 13- Limits and Derivatives, which includes thorough solutions for reference. All of the unsolved questions from the textbook’s exercises are answered here. The NCERT Exemplar Solutions for Class 11 provide useful solutions for improving conceptual knowledge and help in entrance examinations like JEE mains and advanced.
The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 11 pupils perform well in upcoming competitive exams.
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NCERT Exemplar Solutions for Class 11 Maths Chapter 13 – Limits and Derivatives
Chapter 13 of Maths for Class 11 Limits and derivatives are covered individually in CBSE Syllabus 2021-22 as Limits in the term I and Derivatives in term II, and contain the following:
13.1 Introduction
This section introduces the calculus, derivative, limits, and algebra of limits branches of mathematics. Certain standard functions’ derivatives are also examined.
- In electrical engineering, calculus is used to determine the length of wire to be used between two stations that are kilometres apart.
- Calculus is used to determine an object’s velocity and trajectory.
- In operations research, calculus is utilized to increase efficiency, productivity, and profit.
13.2 Intuitive Idea of Derivatives
This section explains how to calculate the derivative of a function using a real-life example of distance travelled at various time intervals.
The derivative refers to the pace at which one quantity changes in relation to another. If you run a business (for example, selling sweets), derivatives can assist you to figure out how much to sell. Data on your company’s performance over the previous few months should be collected, and the trend should be assessed by plotting a curve. The instantaneous slope (dy/dx) of this graph is defined by derivative.
The slope indicates the marginal cost of generating each extra unit at that time (cost change/unit produced change). If this cost exceeds the selling price of ten dollars, a loss is incurred at this moment.
Refer the table given below, for better understanding:
For 0-300 units, if the cost > sales, then it’s a loss
For 400-600 units, if the sales > cost, then it’s a profit
13.3 Limits
This part teaches limitations with an engaging example, as well as the left-hand and right-hand limits, as well as solved issues.
When an ice cube is thrown into a glass of warm water and the temperature is recorded over time, it represents a limit as the time approaches infinity. The temperature steadily reaches the room temperature where the glass was stored during the time period monitored.
13.3.1 Algebra of limits
The output of the sum, difference, product, and quotient of limits is shown in this section.
13.3.2 Limits of polynomials and rational functions
The limits of polynomials and rational functions are discussed in detail, with examples provided.
13.4 Limits of Trigonometric Functions
This section covers function theorems and prepositions, which are useful in determining the limits of several trigonometric functions.
13.5 Derivatives
This section assists students in locating answers to various derivative problems.
Money-related institutions must anticipate changes in the assessment of certain stock based on its current value. In this situation, as well as many others, it’s critical to understand how one parameter changes in relation to another. The derivative of a function at a given point in its domain of definition lies at the heart of the book.
13.5.1 Algebra of derivatives of functions
The result of sum, difference, product, and quotient of derivatives is shown in this section.
13.5.2 Derivative of polynomials and trigonometric functions
Theorems and problems for functions that help compute the derivatives of several trigonometric functions are covered in this section.
Following are the concepts discussed in Chapter 13 Limits and Derivatives:
- The function’s expected value, as determined by the points to the left of a point, determines the function’s left-hand limit at that point. The right-hand limit is similar.
- The common value of the left and right-hand limits if they coincide is the limit of a function at a location.
- For a function f and a real number, a lim x → a f(x) and f (a) may not be the same.
The PDF solutions include a detailed explanation for each problem. Limits and Derivatives NCERT Exemplar Solutions for Class 11 Maths Chapter 13 are at your fingertips. The solutions are designed so that a student understands the split-up marks for each segment, allowing them to determine how much time and effort they should devote to each section of the first and second-term exams. The NCERT Exemplar Solutions have been recommended by high-scoring students as a good source of information on each topic.
Frequently Asked Questions
Can I get the NCERT Exemplar Solutions for Class 11 Maths Chapter 13 in PDF format?
Yes, students can access the NCERT Exemplar Solutions for Class 11 Maths Chapter 13 in ‘Infinity Learn’ in PDF format. The solutions for the exercise-by-exercise difficulties are created by highly experienced faculty using the most up-to-date CBSE Syllabus for each term. Students can also compare their answers to the solutions PDF to acquire a better understanding of the alternative approaches for tackling complicated issues quickly.
Explain the difference between integral calculus and differential calculus as per Chapter 13 of NCERT Exemplar Solutions for Class 11 Maths.
Differential calculus uses functional derivatives to calculate the rate of change of a variety of values across time. Integral calculus deals with antiderivatives and is the polar opposite of differential calculus. Students should keep this idea in mind as they study this chapter since it will help them learn the principles more quickly.
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