Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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### Exercise: Graph of \( f(x) = \cot(x) + 1 \) #### Instructions: 1. **Draw asymptotes as dashed lines on graph.** 2. **Amplitude:** (Leave blank, as cotangent functions do not have an amplitude). 3. **Period:** \( 0 < Bx - C < \pi \) \( \_\_\_\_ < x < \_\_\_\_\_ \) (Fill in the blank intervals). 4. **Domain:** All real numbers except every \_\_\_\_ (period), beginning at \_\_\_\_. 5. **Vertical shift:** (Leave blank, no vertical shift for this function). 6. **Asymptotes:** \( x = \_\_\_\_\_, x = \_\_\_\_\_ \) (Identify the vertical asymptotes for one period). 7. **Point of inflection:** \(( \_\_\_\_\_, \_\_\_\_\_ )\) (Identify if exists). 8. **1/4 and 3/4 points:** \(( \_\_\_\_\_, \_\_\_\_\_ )\) and \(( \_\_\_\_\_, \_\_\_\_\_ )\) (Mark these points on the graph). 9. **Range:** \(\_\_\_\_\_\_\_) (Define the range of the function). 10. **Graph two periods of the curve. Draw the asymptotes as dashed lines.** #### Graph Description: The provided graph shows the \(y\)-axis in the vertical direction and the \(x\)-axis in the horizontal direction. The x-values range from \(-\pi\) to \(2\pi\), and y-values range from \(-3\) to \(4\). Dashed vertical lines indicate the asymptotes where the function is undefined. Points are marked on the curve at regular intervals. Key points to include: - Vertical asymptotes at \( x = 0 \), \( x = \pi \), \( x = 2\pi \), etc. - Increasing behavior of the function \( f(x) \) within each period \((0, \pi)\) and \((\pi, 2\pi)\). - The function values transition smoothly through the points marked on the graph. Feel
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Transcribed Image Text:### Exercise: Graph of \( f(x) = \cot(x) + 1 \) #### Instructions: 1. **Draw asymptotes as dashed lines on graph.** 2. **Amplitude:** (Leave blank, as cotangent functions do not have an amplitude). 3. **Period:** \( 0 < Bx - C < \pi \) \( \_\_\_\_ < x < \_\_\_\_\_ \) (Fill in the blank intervals). 4. **Domain:** All real numbers except every \_\_\_\_ (period), beginning at \_\_\_\_. 5. **Vertical shift:** (Leave blank, no vertical shift for this function). 6. **Asymptotes:** \( x = \_\_\_\_\_, x = \_\_\_\_\_ \) (Identify the vertical asymptotes for one period). 7. **Point of inflection:** \(( \_\_\_\_\_, \_\_\_\_\_ )\) (Identify if exists). 8. **1/4 and 3/4 points:** \(( \_\_\_\_\_, \_\_\_\_\_ )\) and \(( \_\_\_\_\_, \_\_\_\_\_ )\) (Mark these points on the graph). 9. **Range:** \(\_\_\_\_\_\_\_) (Define the range of the function). 10. **Graph two periods of the curve. Draw the asymptotes as dashed lines.** #### Graph Description: The provided graph shows the \(y\)-axis in the vertical direction and the \(x\)-axis in the horizontal direction. The x-values range from \(-\pi\) to \(2\pi\), and y-values range from \(-3\) to \(4\). Dashed vertical lines indicate the asymptotes where the function is undefined. Points are marked on the curve at regular intervals. Key points to include: - Vertical asymptotes at \( x = 0 \), \( x = \pi \), \( x = 2\pi \), etc. - Increasing behavior of the function \( f(x) \) within each period \((0, \pi)\) and \((\pi, 2\pi)\). - The function values transition smoothly through the points marked on the graph. Feel
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