Evaluate the Limit

Problem

(lim_x→3)((2*x2−x−15)/(4*x−12))

Solution

1. Substitute the value x=3 into the expression to check for an indeterminate form.

(2*(3)2−3−15)/(4*(3)−12)=(18−3−15)/(12−12)=0/0

2. Factor the numerator 2*x2−x−15 by finding two numbers that multiply to −30 and add to −1

2*x2−x−15=(2*x+5)*(x−3)

3. Factor the denominator 4*x−12 by taking out the greatest common factor.

4*x−12=4*(x−3)

4. Simplify the expression by canceling the common factor (x−3) from the numerator and the denominator.

((2*x+5)*(x−3))/(4*(x−3))=(2*x+5)/4

5. Evaluate the limit by substituting x=3 into the simplified expression.

(lim_x→3)((2*x+5)/4)=(2*(3)+5)/4

(6+5)/4=11/4

Final Answer

(lim_x→3)((2*x2−x−15)/(4*x−12))=11/4

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