Evaluate the Limit

Problem

(lim_x→−2)(3*x5−3*x4+4*x3+x2+5)

Solution

1. Identify the type of function. The expression 3*x5−3*x4+4*x3+x2+5 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)5−3*(−2)4+4*(−2)3+(−2)2+5

4. Evaluate the powers of −2

3*(−32)−3*(16)+4*(−8)+4+5

5. Multiply the terms.

−96−48−32+4+5

6. Combine the constants to find the final value.

−144−32+9

−176+9=−167

Final Answer

(lim_x→−2)(3*x5−3*x4+4*x3+x2+5)=−167

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