Understanding Limits and Rational Functions

The video tutorial explains how to solve limits involving radicals and rational functions. It covers techniques such as using conjugates to simplify expressions and factoring to cancel terms. The tutorial provides step-by-step examples, demonstrating how to handle undefined expressions and apply direct substitution once simplification is achieved.

What is the first step when you cannot use direct substitution to find a limit?

• Multiply by the conjugate

• Use a calculator

• Add a constant to the expression

• Divide by zero

Why can't direct substitution be used initially in the problem where X approaches 4?

• The expression is too complex

• The function becomes undefined

• The limit does not exist

• The result is a negative number

What is the purpose of multiplying by the conjugate in limit problems?

• To find the derivative

• To change the variable

• To add complexity

• To eliminate radicals

In the problem where X approaches Z, what happens to the middle terms when multiplying by the conjugate?

• They cancel out

• They remain unchanged

• They become zero

• They double

What is the common denominator used for in rational function limits?

• To multiply fractions

• To simplify the expression

• To find the derivative

• To add fractions

When X approaches 3 in a rational function, why is the expression initially undefined?

• The numerator is zero

• The denominator is zero

• The expression is negative

• The expression is positive

What is the result of factoring out the GCF in the rational function example?

• The expression is multiplied by zero

• The expression remains the same

• The expression is simplified

• The expression becomes more complex

In the final example, what is the result of distributing the negative sign?

• The terms are divided

• The terms are multiplied

• The terms are added

• The terms are subtracted

What is the final step in solving the limit problem as X approaches Z?

• Multiply by zero

• Use direct substitution

• Add a constant

• Divide by the variable

What is the final answer for the limit as X approaches Z in the last example?

• 1/4

• -1/9

• -1/4

• 1/9