Question

Use the graph of the greatest integer function \( y=\lfloor x\rfloor \), Figure \( 1.10 \) in Section \( 1.1 \), to help you find the limits in Exercises 19 and 20 . 19. a. \( \lim _{\theta \rightarrow 3^{+}} \frac{\lfloor\theta\rfloor}{\theta} \) b. \( \lim _{\theta \rightarrow 3^{-}} \frac{\lfloor\theta\rfloor}{\theta} \) 20. a. \( \lim _{t \rightarrow 4^{+}}(t-\lfloor t\rfloor) \) b. \( \lim _{t \rightarrow 4^{-}}(t-\lfloor t\rfloor) \)

          Use the graph of the greatest integer function \( y=\lfloor x\rfloor \), Figure \( 1.10 \) in Section \( 1.1 \), to help you find the limits in Exercises 19 and 20 .
19. a. \( \lim _{\theta \rightarrow 3^{+}} \frac{\lfloor\theta\rfloor}{\theta} \)
b. \( \lim _{\theta \rightarrow 3^{-}} \frac{\lfloor\theta\rfloor}{\theta} \)
20. a. \( \lim _{t \rightarrow 4^{+}}(t-\lfloor t\rfloor) \)
b. \( \lim _{t \rightarrow 4^{-}}(t-\lfloor t\rfloor) \)

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Use the graph of the greatest integer function y=⌊ x⌋, Figure 1.10 in Section 1.1, to help you find the limits in Exercises 19 and 20 .
19. a. limθ→ 3^+(⌊θ⌋)/(θ)
b. limθ→ 3^-(⌊θ⌋)/(θ)
20. a. limt → 4^+(t-⌊ t⌋)
b. limt → 4^-(t-⌊ t⌋)

Added by Amr A.

Thomas' Calculus: Early Transcendentals in SI Units

George B. Thomas Jr., Maurice D. Weir,… 13th Edition

Chapter 2

Instant Answer

Solved by Expert Stephen Hobbs

08/06/2020

Step 1

a. As \( \theta \) approaches 3 from the right, the greatest integer function \( \lfloor \theta \rfloor \) will be equal to 3. So, the expression becomes \( \frac{3}{\theta} \). As \( \theta \) approaches 3, the expression approaches \( \frac{3}{3} \), which is 1. Show more…

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