Analyze the following limits. Then sketch a graph of y=tanx with the window [−π,π]×[−10,10]and use your graph to check your work.
lim x→π/2^− tan x

Key Concepts

Limits

A limit is a fundamental concept in calculus that describes the behavior of a function as its input approaches a certain value. It helps in understanding the function's behavior near points of interest, including points where the function may not be defined. For example, the limit of tan(x) as x approaches π/2 from the left indicates how the function behaves as it nears this vertical asymptote.

Vertical Asymptotes

Vertical asymptotes occur in functions where the function approaches infinity or negative infinity as the input approaches a certain value. For the tangent function, vertical asymptotes are found at odd multiples of π/2, where the function is undefined. Understanding vertical asymptotes is crucial for analyzing the limits of functions like tan(x) and for sketching accurate graphs.

Graphing Trigonometric Functions

Graphing trigonometric functions, such as y = tan(x), involves understanding their periodic nature and key features like asymptotes, intercepts, and periodicity. The tangent function has a period of π and exhibits vertical asymptotes at odd multiples of π/2. By sketching the graph within a specified window, one can visually confirm the behavior of the function and the accuracy of calculated limits.