Evaluate the Limit

Problem

(lim_x→−∞)(x6+x7)

Solution

1. Identify the highest power of x in the polynomial, which is x7

2. Factor out the highest power term to analyze the behavior of the expression as x grows large.

x6+x7=x7*(1/x+1)

3. Evaluate the limit of each part of the product as x→−∞

(lim_x→−∞)(x7)=−∞

(lim_x→−∞)(1/x+1)=0+1=1

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

(−∞)⋅(1)=−∞

Final Answer

(lim_x→−∞)(x6+x7)=−∞

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