Evaluate the Limit

Problem

(lim_x→−∞)(x^2+x^3)

Solution

1. Identify the highest power of x in the polynomial, which is x^3

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

(lim_x→−∞)(x^3)*(1+1/x)

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

(lim_x→−∞)(1+1/x)=1+0=1

4. Determine the behavior of the leading term x^3 as x approaches negative infinity.

(lim_x→−∞)(x^3)=−∞

5. Multiply the results of the limits.

(−∞)⋅(1)=−∞

Final Answer

(lim_x→−∞)(x^2+x^3)=−∞

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