Evaluate the Limit limit as x approaches 2 of 3x^2-5x+2

Problem

(lim_x→2)(3*x2−5*x+2)

Solution

1. Identify the type of function. The expression 3*x2−5*x+2 is a polynomial.

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

3. Substitute x=2 into the expression.

3*(2)2−5*(2)+2

4. Simplify the arithmetic by calculating the exponent first.

3*(4)−5*(2)+2

5. Multiply the terms.

12−10+2

6. Combine the remaining values to find the final result.

2+2=4

Final Answer

(lim_x→2)(3*x2−5*x+2)=4

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