Find the limit.limx→0−(x8x4+2x)

To find the limit of the function as x approaches 0, we can use the rule of l'Hopital, which states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

The function is given as f(x) = x^8 / (x^4 + 2x).

Step 1: Differentiate the numerator and the denominator. The derivative of x^8 is 8x^7. The derivative of x^4 + 2x is 4x^3 + 2.

Step 2: Apply l'Hopital's rule. lim (x→0) [f'(x) / g'(x)] = lim (x→0) [8x^7 / (4x^3 + 2)]

Step 3: Evaluate the limit. As x approaches 0, the function approaches 0/2 = 0.

So, the limit of the function as x approaches 0 is 0.