Use baby numbers to evaluate the right hand limit of a rational function

The video tutorial explores the concept of limits in calculus, focusing on direct substitution and its failure in certain cases. It then examines factoring as an alternative approach, but highlights its limitations. The tutorial proceeds to analyze the left hand limit, noting the presence of an asymptote at x=4, which leads to the graph approaching infinity or negative infinity. The right hand limit is calculated by choosing a number close to four, and sign analysis is used to determine the behavior of the limit, concluding with the result of negative infinity.

Why does direct substitution fail in some limit problems?

• Because the function is differentiable

• Because the function is continuous

• Because it results in an indeterminate form

• Because it simplifies the expression

What is the purpose of factoring in solving limits?

• To find the derivative

• To change the variable

• To simplify the expression

• To eliminate discontinuities

What happens to the graph of a function at an asymptote?

• It remains constant

• It oscillates between two values

• It approaches infinity or negative infinity

• It becomes a straight line

How do you determine the limit from the right-hand side?

• By choosing a number slightly less than the point

• By using direct substitution

• By choosing a number slightly greater than the point

• By factoring the expression

What is the result of a negative over a positive in limit analysis?

• Negative infinity

• Positive infinity

• Undefined

• Zero