Left hand Limit of a rational function at a hole

The video tutorial discusses the concept of limits, focusing on approaching a point from the left. It covers factoring trinomials to better understand functions, identifying holes and asymptotes in graphs, and analyzing graph behavior near asymptotes. The tutorial concludes with calculating limits using direct substitution, emphasizing the importance of simplifying expressions before applying substitution.

What is the first step suggested by the speaker when dealing with a trinomial in a limit problem?

• Check for continuity

• Use a graphing calculator

• Apply direct substitution

• Factor the trinomial

What does the speaker identify at X = 1 and X = 4 in the function?

• An intercept and a vertex

• A tangent and a secant

• A maximum and a minimum

• A hole and an asymptote

Why does the speaker suggest using a graphing calculator?

• To visualize the graph and understand asymptotes and holes

• To check for errors in calculations

• To find the exact value of the limit

• To determine the domain of the function

What is the significance of left and right-hand limits at an asymptote?

• They indicate whether the graph approaches infinity or negative infinity

• They help in finding the intercepts

• They show the continuity of the function

• They determine the slope of the tangent

What is the final value approached by the function as X approaches the hole from the left?

• 0

• 5/3

• 1/3

• -5/3