Understanding Basic Limits

The video tutorial covers four examples of determining basic limits. It begins with a constant function, explaining how limits can be determined using direct substitution when the function is continuous. The second example uses the identity function, demonstrating the same principle. The third example involves a linear function, and the fourth example uses a polynomial function. Each example is explained with graphical representation, emphasizing the concept of continuity and direct substitution in limit determination.

What is the limit of a constant function as x approaches any value?

• The limit is undefined.

• The limit depends on the value of x.

• The limit is the constant value itself.

• The limit is always 0.

When can direct substitution be used to find the limit of a function?

• When the function is a constant.

• When the function is continuous over an open interval containing the point.

• When the function is discontinuous.

• When the function is undefined at the point.

What is the limit of the identity function f(x) = x as x approaches 3?

• 0

• 1

• 3

• Undefined

Why is the identity function continuous over all real numbers?

• Because it is a linear function.

• Because it is a quadratic function.

• Because it is a polynomial function.

• Because it is a constant function.

What is the limit of the function f(x) = -2x + 3 as x approaches 4?

• 3

• 5

• 0

• -5

How can the limit of a linear function be determined?

• By using the derivative.

• By using limits at infinity.

• By using direct substitution.

• By using integration.

What is the limit of the polynomial function f(x) = 0.5x^3 + x^2 as x approaches 0?

• 0

• 0.5

• 1

• Undefined

Why are polynomial functions continuous over all real numbers?

• Because they are composed of constant terms.

• Because they are composed of rational terms.

• Because they are composed of linear terms.

• Because they are composed of powers of x.

What is the significance of continuity in determining limits?

• It allows for the use of integration.

• It allows for the use of direct substitution.

• It allows for the use of limits at infinity.

• It allows for the use of derivatives.

Which of the following functions is always continuous over all real numbers?

• Trigonometric functions

• Rational functions

• Exponential functions

• Polynomial functions