Question

Evaluate the limit lim x→-2 (2x² + ax)/(a⁶x²(x - 2)).

Answer 1

To evaluate the limit, we can simplify the expression by canceling out x - 2 in the denominator. Next, we can factor out x² from the numerator and the denominator. Since the x² terms cancel out, the limit becomes (2 + a)/(a⁶).

Step-by-step explanation:

To evaluate the limit lim x→-2 (2x² + ax)/(a⁶x²(x - 2)), we can simplify the expression by canceling out x - 2 in the denominator, as the value of x will be significantly less than 2. This simplification results in lim x→-2 (2x² + ax)/(a⁶x²). Next, we can factor out x² from the numerator and the denominator, giving us lim x→-2 (x²(2 + a))/(x²(a⁶)). Since the x² terms cancel out, the limit becomes lim x→-2 (2 + a)/(a⁶).