Evaluate the Limit

Problem

(lim_n→∞)((6*n2+5)/(3*n2))

Solution

1. Identify the type of limit, which involves a rational function where the variable n approaches infinity.

2. Divide every term in the numerator and the denominator by the highest power of n found in the denominator, which is n2

3. Simplify the expression by canceling out the n2 terms.

((6*n2)/(n2)+5/(n2))/(3*n2)/(n2)

4. Reduce the fractions to their simplest form.

(6+5/(n2))/3

5. Apply the limit laws, noting that as n approaches infinity, the term 5/(n2) approaches 0

(6+0)/3

6. Calculate the final numerical value.

6/3=2

Final Answer

(lim_n→∞)((6*n2+5)/(3*n2))=2

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