Sample Problems
Question 1: Find out the following limit.
Solution:
This limit is of the 0/0 form. Factorization can be used here.
⇒
⇒
⇒
⇒
⇒
⇒
Question 2: Find out the following limit.
Solution:
This limit is of the 0/0 form. Factorization can be used here.
⇒
⇒
⇒
⇒
⇒ -1
Question 3: Find out the following limit.
Solution:
This limit is of the indeterminate form. Rationalization can be used here.
Question 4: Find out the limit of,
Solution:
Putting the limit x tends to 2 to see the value obtained,
= Undefined.
As, it is clear that the answer is undefined, rationalize the denominator,
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Determining Limits using Algebraic Manipulation
Limits give us the power to approximate functions and see the values they are approaching. Limit is not the value of the function at a particular point. It is the value which the function is approaching as one moves towards the given point. There are many ways to solve the limits, often limits are easy to solve, but sometimes they evaluate into indeterminate forms which are not defined and are difficult to estimate. The goal is to avoid these forms and solve the limits of the function. Let’s look at some algebraic ways to solve such limits.
Table of Content
- Limits
- Indeterminate Forms
- Limits using Algebraic Manipulation
- Limits by Factoring
- Limits by Rationalization
- Trigonometric limits using Pythagorean Identities
- Double angle Identities
- Sample Problems
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