Evaluate the limit of a piecewise function

The video tutorial explains how to determine the limit of a function as X approaches zero. It emphasizes that for a limit to exist, the left-hand and right-hand limits must be equal. The tutorial demonstrates calculating these limits using the functions X^3 and sqrt(X) and shows that direct substitution can be used since both functions are continuous. The conclusion is that the limit is zero as both sides approach zero.

What must be true for a limit to exist at a point?

• The function must be differentiable at that point.

• The left-hand limit and right-hand limit must be equal.

• The function must be continuous everywhere.

• The function must be defined only on the left side of the point.

Which function is used to determine the left-hand limit as X approaches zero?

• X^3

• Square root of X

• 1/X

• X^2

What function is used to find the right-hand limit in this problem?

• X^2

• 1/X

• X^3

• Square root of X

Why can we use direct substitution to find the limit in this scenario?

• Because the functions are differentiable.

• Because the functions are periodic.

• Because the functions are continuous.

• Because the functions are integrable.

What is the final value of the limit as X approaches zero?

• 1

• Undefined

• Infinity

• 0