Rahul Anand

A Python code to generate a number line image using matplotlib. import matplotlib.pyplot as plt import numpy as np import matplotlib.font_manager as fm # Path to your font file (e.g., Helvetica) font_path = r'D:\Rahul\Websites\fonts\LUNCH.ttf' # Create a FontProperties object font_prop = fm.Fon

As angles get incredibly small, a fascinating mathematical phenomenon occurs. The ratio of the sine of an angle to the angle itself converges to one. This intriguing property reveals the close relationship between sine and angles in the realm of trigonometry.

Find \( \lim_{x \to 3} (2x + 5) \) Solution: To solve this limit, we substitute the value of \( x \) directly because the function is continuous at \( x = 3 \).\( \lim_{x \to 3} (2x + 5) = 2(3) + 5 = 6 + 5 = 11 \)