Evaluate the Limit limit as x approaches 0 of x^2+1

Problem

(lim_x→0)(x2+1)

Solution

1. Identify the type of function. The expression x2+1 is a polynomial.

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

3. Substitute the value x=0 into the expression.

0+1

4. Simplify the result.

0+1=1

Final Answer

(lim_x→0)(x2+1)=1

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