Find the limit
limit as x approaches 1 of (2-x)^3tan[(pi/2)x]
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,, =)
To find the limit as x approaches 1 of the expression (2-x)^3tan[(π/2)x], you can apply the limit rules and evaluate the limit step by step.
Step 1: Substitute the value of x into the expression.
Replace x with 1 in the given expression:
(2 - 1)^3 * tan[(π/2)(1)]
Simplifying the expression:
(1)^3 * tan[(π/2)(1)]
tan(π/2)
Step 2: Evaluate the trigonometric function.
The tangent of π/2 is undefined.
Therefore, the limit as x approaches 1 of (2-x)^3tan[(π/2)x] is undefined.