Hi! My name is Maria a full-time online tutor for 6 years. I'm very passionate and patient especially when tutoring. I've always wanted to share what I learned and to keep learning as well.
I was an instructor at a college institution in the Philippines. I was teaching algebra, trigonometry and geometry. Then I became a teaching assistant in my previous school. I was teaching and studying at the same time for my Master's degree. I also became a substitute teacher in a secondary school. I was teaching algebra and calculus.
The point $ P(1, 0) $ lies on the curve $ y = \sin (10\pi /x) $.
(a) If $ Q $ is the point $ (x, \sin (10\pi /x)) $, find the slope of the secant line $ PQ $ (correct to four decimal places) for $ x $ = 2, 1.5, 1.4, 1.3, 1.2, 1.1, 0.5, 0.6, 0.7, 0.8, and 0.9 .
Do the slopes appear to be approaching a limit?
(b) Use a graph of the curve to explain why the slopes of the secant lines in part (a) are not close to the slope of the tangent line at $ P $.
(c) By choosing appropriate secant lines, estimate the slope of the tangent line at $ P $.