Find the limit
limit as x approaches 1 of (2-x)^3tan[(pi/2)x]
To find the limit as x approaches 1 of the given expression, (2-x)^3tan[(pi/2)x], we can follow these steps:
Step 1: Substitute the value x = 1 into the expression.
(2-1)^3tan[(pi/2)(1)]
Simplifying this gives us:
1^3tan[pi/2]
Step 2: Evaluate the tangent function.
Recall that the tangent of pi/2 is undefined.
Therefore, the limit as x approaches 1 of (2-x)^3tan[(pi/2)x] is undefined.