Evaluate..........Please Help
Lim Infinite -> 0 Infinite/cos infinite
What approaches zero? Your expression makes no sense to me.
Sorry I posted the incorrect ?
Evaluate: Theta approached zero
Theta/cos theta
To evaluate the limit of (infinite / cos(infinite)) as infinity approaches 0, we can use L'Hôpital's Rule. This rule applies when we have an indeterminate form, like infinite over infinite.
First, let's rewrite the expression as (1 / cos(infinite)) / (1 / infinite). Now, we can rewrite it as (infinite / 1) / (cos(infinite) / 1).
Using L'Hôpital's Rule, we take the derivative of the numerator and denominator separately. The derivative of infinite is still infinite, and the derivative of cos(infinite) is -sin(infinite).
So, the expression becomes (infinite / 1) / (-sin(infinite) / 1).
Now, we can simplify it as -infinite * (1 / sin(infinite)), since dividing by a fraction is equivalent to multiplying by its reciprocal.
As we approach 0, the sin(infinite) term will oscillate between -1 and 1, but its magnitude will not change. Thus, the expression becomes -infinite * (1 / sin(infinite)) = -infinite * (1 / 1) = -infinite.
Therefore, the limit of (infinite / cos(infinite)) as infinity approaches 0 is -infinite.