Find the limit

limit as x approaches 1 of (2-x)^3tan[(pi/2)x]

3 answers

what does tan PI/2 approach.
it is all one equation, it's (2-x)to the power of 3tan[(pi/2)x]
substitute the value of x:
(2-1)^3tan[pi/2] = 1^3tan[pi/2]

note: 3*tan (pi/2) = 3*[sin(pi/2)]/[cos(pi/2)] = 3/0 = infinity

therefore, 1^infinity = 1

so there,, =)