Evaluate the Limit

Problem

(lim_x→8)((5*x2+7*x−9)/(−6*x2+2))

Solution

1. Identify the type of limit by checking if the denominator is zero at the target value x=8

2. Substitute the value x=8 into the expression, as the function is a rational function and the denominator −6*(8)2+2 is not zero.

3. Calculate the numerator by evaluating 5*(8)2+7*(8)−9

5*(64)+56−9

320+56−9=367

4. Calculate the denominator by evaluating −6*(8)2+2

−6*(64)+2

−384+2=−382

5. Simplify the resulting fraction if possible.

Final Answer

(lim_x→8)((5*x2+7*x−9)/(−6*x2+2))=−367/382

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