Limits: Overview, Questions, Preparation

A limit is a value that a particular function approaches as the independent variable’s value in the function approaches a certain quantity. It is the first stepping stone toward concepts such as derivatives and integrals. Limits are expressed using the word ‘lim’. The value of the independent variable is noted below the word ‘lim’, and the function is noted after it.

For a real-valued function f(x), if the value of x tends toward the real number c, the limit is expressed in the following way.

lim_{x →c}f(x) = Z

There are specific rules that govern the functions of limits. Here is a list of the properties that are common to all limits.

The topic of limits is extremely essential for understanding more about calculus in further chapters. Hence, the topic is taught in great detail and over multiple classes, and also has a chapter devoted to it. A number of examples are provided to give students a more fundamental understanding of the topic on limits. From the examination point of view, limits can carry a weightage of up to 10 marks in Class XI. It can be evaluated in questions of 1, 2, 4, or 6 marks.

1. What is the value of lim _x→2x² + 2x + 5
Solution. lim _x→2x²+ 2x + 5
= lim _x→2x² + lim _x→22x +lim _x→2 5
= 2² + 2(2) + 5
= 13

2.What is the value of lim _x→2(x²-4)/(x-2)?
Solution. lim _x→2(x²-4)/(x-2)
=lim _x→2(x-2)(x+2)/(x-2)
=lim _x→2(x+2)
=2+2
=4

3.What is the value of lim _x→2(x²-5x +6)/(x-2)?
Solution. lim _x→2(x²-5x +6)/(x-2)
=lim _x→2(x-2)(x+3)/(x-2)
=lim _x→2(x+3)
=2+3
=5

Q: How do you read out a limit function?

Q: What is the limit of a constant value?

Q: Can undefined values have limits?

Q: What is the sum of two limited functions?

Q: What is the limit of a function that is defined at a value?