Evaluate the Limit

Problem

(lim_x→∞)(ƒ(x)+2*g(x))

Solution

1. Apply the sum rule for limits, which states that the limit of a sum is the sum of the limits.

(lim_x→∞)(ƒ(x)+2*g(x))=(lim_x→∞)(ƒ(x))+(lim_x→∞)(2)*g(x)

2. Apply the constant multiple rule for limits to the second term, moving the coefficient outside the limit.

(lim_x→∞)(ƒ(x))+(lim_x→∞)(2)*g(x)=(lim_x→∞)(ƒ(x))+2*(lim_x→∞)(g(x))

3. Evaluate the expression by substituting the specific limit values for ƒ(x) and g(x) as x approaches infinity.

Final Answer

(lim_x→∞)(ƒ(x)+2*g(x))=(lim_x→∞)(ƒ(x))+2*(lim_x→∞)(g(x))

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