Chapter - 15
Limits and Continuity
We will mostly study about the techniques for determining the limits of normal functions and trigonometric functions in this chapter. We will also learn how to determine whether a function is continuous or discontinuous. In our previous exercise, we had learnt how to find the limits of a normal function and a trigonometric function. You should review the preceding exercise if you haven't before moving forward to next exercise.
Today, in this particular exercise we will only learn how to find the right hand limit, left hand limit, functional value and to check whether the given function is continuous or discontinuous.
Right hand limit
A function f(x) is said to have the right hand limit l₁ at x = a as x approaches a through value greater than a (i.e. x approaches a from the right) and symbolically it is written as limₓ→ₐ+ f(x) = l₁. The right hand limit of f(x) at x = a is also written as limₓ→ₐ+⁰ f(x) f(a + 0).
Left hand limit
A function f(x) is said to have the right hand limit l₂ at x = a as x approaches a through value less than a (i.e. x approaches a from the left) and symbolically it is written as limₓ→ₐ- f(x) = l₂. The left hand limit of f(x) at x = a is also written as limₓ→ₐ-⁰ f(x) f(a - 0).
Continuity of a Function
The intuitive idea of a continuous functions f in the interval [a, b] gives the impression that the graph of the function f in this interval is a smooth curve without any break in it. Actually this curve is such that it can be drawn by the continuous motion of pencil without lifting it in a sheet of paper. Similarly, a discontinuous function gives the picture consisting of disconnected curves.
Exercise - 15.3
This PDF contains all of the class 11 Limits and Continuity Chapter solutions. It only contains exercise solutions - 15.3. If you're looking for solutions to exercise - 15.1 and exercise - 15.2, look no further. All you have to do is click on the button above.
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Is Class 11 Mathematics Guide Helpful For Student ?
I created these notes to assist students who struggle to solve challenging math problems. The student should not completely rely on this note to finish all of the exercises. It may affect your study if you rely solely on this note and simply copy it as written.
Students should also try to solve problems themselves by using their own willpower. You can utilize this math guide PDF as a kind of perspective. Before copying, you should make sure that all of the answers are correct. The note may contain some minor errors; please take those errors into consideration.
How to secure good marks in Mathematics ?
You may be aware that I am also a student. It's hard to be a student. You have to study multiple subjects at the same time. The majority of students, in my opinion, lack mathematical proficiency. You can use my weakness in mathematics as an illustration. When I attempt to solve math problems, I also encounter difficulties.
You should practice them every day if you want to get good grades in mathematics. You should go over every exercise that was taught in class once more. Start with simple questions that you already know to solve math problems. You won't get bored if you do this.
Math is more than just practicing; especially in 11th grade, you need to understand the problem's fundamentals. When you understand the problem's fundamental idea, you can quickly identify other problems with a similar approach.
Every student tries to remember the same example when your teacher tries to make the concept clear by giving examples, but you should never do that. You can come up with your own formula that you won't forget in the future.
You can definitely get good grades on your exam if you practice properly and give yourself enough time to do so.
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