Evaluate the Limit limit as n approaches 8 of 5n^2-15

Problem

(lim_n→8)(5*n2−15)

Solution

1. Identify the type of function. The expression 5*n2−15 is a polynomial.

2. Apply the direct substitution property for limits. Since polynomials are continuous everywhere, the limit as n approaches a value is equal to the function evaluated at that value.

3. Substitute the value n=8 into the expression.

5*(8)2−15

4. Calculate the square of 8.

5*(64)−15

5. Multiply 5 by 64.

320−15

6. Subtract 15 from 320 to find the final value.

305

Final Answer

(lim_n→8)(5*n2−15)=305

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