Evaluate the Limit limit as x approaches 2 of x^3+5x^2-7x+1

Problem

(lim_x→2)(x3+5*x2−7*x+1)

Solution

1. Identify the type of function. The expression x3+5*x2−7*x+1 is a polynomial.

2. Apply the Direct Substitution Property for limits. Since polynomials are continuous everywhere, the limit as x approaches a is simply the value of the function at a

3. Substitute the value x=2 into the expression.

2+5*(2)2−7*(2)+1

4. Simplify the terms by performing the arithmetic operations.

8+5*(4)−14+1

8+20−14+1

28−14+1

14+1=15

Final Answer

(lim_x→2)(x3+5*x2−7*x+1)=15

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