Find the limit if it exist lim t-->pi/3 (tan(t)/t)+1
To find the limit of a function as a variable approaches a certain value, we substitute the value into the function and calculate the resulting value. If the resulting value approaches a finite number as the variable gets closer and closer to the given value, then the limit exists.
In this case, we need to find the limit as t approaches π/3 of the function (tan(t)/t) + 1.
To calculate this limit, we'll substitute π/3 into the function and simplify:
lim (t → π/3) (tan(t)/t) + 1
= tan(π/3)/(π/3) + 1
We know that tan(π/3) is equal to the square root of 3, and π/3 divided by π/3 is equal to 1.
Therefore, the limit is:
= sqrt(3) + 1
So, the limit as t approaches π/3 of the given function is sqrt(3) + 1.