Evaluate: 2 212 4lim 5 4 3 3 2xx xx x x x         

To evaluate the given expression, we need to substitute the value of x as it approaches 2.

Step 1: Substitute x = 2 into the expression: (2^2 + 2^1 + 2^4) / (5^3 + 4^2 - 3^3 + 2^2)

Step 2: Simplify the numerator: (4 + 2 + 16) / (5^3 + 4^2 - 3^3 + 2^2)

Step 3: Simplify the denominator: (4 + 2 + 16) / (125 + 16 - 27 + 4)

Step 4: Simplify the numerator further: 22 / (125 + 16 - 27 + 4)

Step 5: Simplify the denominator further: 22 / (118)

Step 6: Evaluate the expression: 22 / 118 = 0.1864 (rounded to four decimal places)

Therefore, the value of the given expression as x approaches 2 is approximately 0.1864.