Yes, it does.
The limit of cos2(x)/x as x approaches 0 does not exist. As x approaches 0 from the left, the limit is negative infinity. As x approaches 0 from the right, the limit is positive infinity. These two values would have to be equal for a limit to exist.
The limit is the Golden ratio which is 0.5[1 + sqrt(5)]
In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)In the limit, a chord approaches a tangent, but is never actually a tangent. (In much the same way as 1/x approaches 0 as x increases, but is never actually 0.)
Because it leads to the limit concept which in turn leads to concept of derivative...
No.
The limit is 0.
1
The limit does not exist.
the limit does not exist
The tangent of infinity is undefined because it is not a real number. The tangent function is defined as the ratio of the side opposite a given angle to the side adjacent to the angle in a right triangle. Since infinity is an abstract concept which has no physical representation, it is not possible to measure the sides of a triangle with an infinite length. Therefore, the tangent of infinity is undefined.
The limit should be 0.
As x goes to infinity, the limit does not exist.