Evaluate the Limit

Problem

(lim_x→−∞)(x6+2*x9)

Solution

1. Identify the highest power of x in the polynomial, which is x9

2. Factor out the highest power term to analyze the behavior of the expression as x approaches negative infinity.

(lim_x→−∞)(x9)*(x(−3)+2)

3. Evaluate the limit of each part of the product.

(lim_x→−∞)(x9)=−∞

(lim_x→−∞)(1/(x3)+2)=0+2=2

4. Multiply the results of the limits to find the final behavior.

(−∞)⋅2=−∞

Final Answer

(lim_x→−∞)(x6+2*x9)=−∞

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