mtayab1994 said:
tiny-tim said:ah!
yes, cos x = 1 - x2/2 + x4/4! - x6/6! + …
you'll learn about that later
The limit of a function involving cosine is the value that the function approaches as the input approaches a specific value, known as the limit point. This can be represented using mathematical notation as lim f(x) = L, where x approaches the limit point and L is the limit value.
To evaluate a limit involving cosine, you can use algebraic manipulation, trigonometric identities, and the limit laws. You can also use a graphing calculator or a table of values to estimate the limit value.
There are three common types of limits involving cosine: limits at a finite point, limits at infinity, and limits involving trigonometric identities. Limits at a finite point involve finding the limit of a function as the input approaches a specific value. Limits at infinity involve finding the limit of a function as the input approaches positive or negative infinity. Limits involving trigonometric identities involve using trigonometric identities to simplify the function and then evaluating the limit.
If a limit involving cosine results in an indeterminate form, such as 0/0 or ∞/∞, you can use L'Hôpital's rule to solve it. This rule states that if the limit of two functions is indeterminate, then the limit of their derivatives will be the same as the original limit. By taking the derivative of the numerator and denominator separately, you can often simplify the function and evaluate the limit.
Limits involving cosine have various applications in physics, engineering, and other fields. One example is in calculating the acceleration of a moving object by taking the limit of its velocity as time approaches zero. This is known as finding the instantaneous rate of change. Other applications include determining the maximum height of a projectile or finding the displacement of a vibrating object.