1. Limits and Continuity

[Technology Exercise] Graph the functions in Exercises 113 and 114. Then answer the following questions.

b. How does the graph behave as x → ±∞?

Give reasons for your answers.

y = (3/2)(x / (x − 1))²/³

Using the Formal Definition

Prove the limit statements in Exercises 37–50.

limx →4 (9 − x) = 5

Determine the end behavior of the following transcendental functions by analyzing appropriate limits. Then provide a simple sketch of the associated graph, showing asymptotes if they exist. 

$f\left(x\right)=\sin x$

Using the Formal Definition

Prove the limit statements in Exercises 37–50.

lim x→0 x sin (1/x) = 0

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Domains and Asymptotes

Determine the domain of each function in Exercises 69–72. Then use various limits to find the asymptotes.

y = 4 + 3x² / (x² + 1)

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