Evaluate the Limit limit as x approaches 0 of 1-(x^2)/6

Problem

(lim_x→0)(1−(x2)/6)

Solution

1. Identify the type of function. The expression 1−(x2)/6 is a polynomial, which is continuous for all real numbers.

2. Apply the direct substitution property for limits. Since the function is continuous at x=0 the limit can be found by evaluating the function at that point.

3. Substitute x=0 into the expression.

1−0/6

4. Simplify the resulting numerical expression.

1−0=1

Final Answer

(lim_x→0)(1−(x2)/6)=1

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