Limit represents the value which function approaches as input. Using limit we can solve different Functions such as continuity function, integrals etc. Now we will see how to solve limits of trigonometric functions.
There are many methods for solving limits of Trigonometry function, it depends on the function. We will use some important steps to solve the trigonometry functions.
Step 1: First we have to take a trigonometry function.
Step 2: Then we will use factoring method to solve trigonometry function using Algebra and conjugate multiplication.
Step 3: At last apply the limit of function and solve the given expression.
Now we will understand it with help of an example.
Example: Find the limit of expression lim j⇢3, k⇢4 [6j2k / j2 + k2 + 9]?
Here given limits are j ⇢3 and k ⇢4 then find the limit for variable “j” and “k”?
Solution: Given expression is: lim j⇢3, k⇢4[6j2k / j2 + k2 + 9];
Given limit are: Limits are j ⇢3 and k ⇢4;
This expression can also be written as:
lim j⇢3, k⇢4[6j2k / j2 + k2 + 9];
We can also write above expression as:
⇒limj⇢3, [lim k⇢4 6j2k / j2 + k2 + 9];
Now put the value of k = 4 in the given expression:
⇒limj⇢3, [limk⇢4 6j2k / j2 + k2 + 9];
On putting the value of k = 4 we get:
⇒lim j⇢3, 6j2 (4) / j2 + (4)2 + 9;
On further solving the expression we get:
⇒lim j⇢3, 24j2 / j2 + 16 + 9;
⇒lim j⇢3, 24j2 / j2 + 25;
Now we have to find value of ‘j’, in the given expression put the value of ‘j’ as 2.
⇒limj⇢3, 24j2 / j2 + 25;
On putting the limit in the above expression, we get:
⇒24 (2)2 / (2)2 + 25;
On moving ahead we get:
⇒24 * 4/ 4 + 25;
⇒ 96 / 29;
After solving all limits we get 3.31.