The NCERT Solutions For Class 11 Maths Chapter 13 Limits and Derivatives are arranged topic wise in a systematic manner. The NCERT Solutions are authored by the most experienced educators in the teaching industry, writing the solutions for every problem in a simpler way. These solutions pdf comes handy for a Class 11 student to understand the idea of Limits and Derivatives.
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NCERT Solutions for Class 11 Maths Chapter 13- Limits and Derivatives
Class 11 Maths Chapter 13 Limits and Derivatives of NCERT Solutions include the following:
13.1 Introduction
This section introduces the branch of mathematics called calculus, derivative, limits and algebra of limits. Derivatives of certain standard functions are also discussed.
- Calculus is used in electrical engineering to find the length of wire to be used between two stations which are miles apart.
- Calculus is used to find the velocity and trajectory of an object.
- Calculus is used in operations research to improve efficiency, productivity and earn profits.
13.2 Intuitive Idea of Derivatives
This section defines the derivative of a function by giving a real-life example of distance travelled at different intervals of time.Â
The derivative is the rate of change at which one quantity varies concerning another. If you run a business (say selling candies), derivatives can help you decide what quantity you should sell. The data of your business performance over the past few months is to be taken and the trend needs to be analyzed by plotting a curve. Derivative defines the instantaneous slope (dy/dx) of this graph.Â
The slope gives an idea of the marginal cost (change in cost/change in unit produced) of producing every additional unit at that instant. If this cost is greater than 10 bucks that is the selling price, then a loss is incurred at the point.
For better clarity, refer to the table given below.
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 profitÂ
13.3 Limits
This section explains limits with an interesting example, left-hand limit and right-hand limit with solved problems.
If an ice cube is dropped into a glass of warm water and the temperature is measured with time, it is an example of limit as the time approaches infinity. The time measured here is the temperature slowly attaining the room temperature where the glass was stored.
13.3.1 Algebra of limits
This section demonstrates the output of sum, difference, product and quotient of limits.Â
13.3.2 Limits of polynomials and rational functions
The limits of polynomials and rational functions are elaborated along with solved examples.
13.4 Limits of Trigonometric Functions
This section deals with the theorems and prepositions for functions, which are helpful in calculating the limits of some trigonometric functions.
13.5 Derivatives
This section helps the student to find solutions on different derivative problems.
Money related establishments need to anticipate the adjustments in the estimation of a specific stock knowing its present worth. In this, and numerous such cases, it is important to know how a specific parameter is changing in accordance with the other parameter. The heart of the text is derivative of a function at a given point in its domain of definition.
13.5.1 Algebra of derivatives of functions
This section demonstrates the output of sum, difference, product and quotient of derivatives.
13.5.2 Derivative of polynomials and trigonometric functions
This section deals with the theorems and problems for functions which help calculate the derivatives of some trigonometric functions.
Exercise 13.1 Solutions 32 Questions
Exercise 13.2 Solutions 11 Questions
Miscellaneous Exercise On Chapter 13 Solutions 30 Questions
A few points on Chapter 13 Limits and Derivatives
- The expected value of the function, as dictated by the points to the left of a point defines the left-hand limit of the function at that point. Similarly the right-hand limit.
- Limit of a function at a point is the common value of the left and right-hand limits if they coincide.
- For a function f and a real number, a lim x → a f(x) and f (a) may not be the same.
The solutions given in the pdf contain a definite clarification for each problem. The NCERT Solutions for Class 11 Maths Chapter 13 Limits and Derivatives are accessible on your fingertips!! The solutions are set up so that a student will have a comprehension of the split-up marks for every part, which thus benefits them to identify the time and energy they need to allocate to every section. High scoring students have suggested NCERT solutions to get sound information on each topic.