Evaluate the Limit

Problem

(lim_x→−∞)(x2+x3)

Solution

1. Identify the highest power of x in the polynomial, which is x3

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

(lim_x→−∞)(x3)*(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 x3 as x approaches negative infinity.

(lim_x→−∞)(x3)=−∞

5. Multiply the results of the limits.

(−∞)⋅(1)=−∞

Final Answer

(lim_x→−∞)(x2+x3)=−∞

Want more problems? Check here!