题目
题目

MAT135H5_F25_ALL SECTIONS 3.5 Preparation Check

单项选择题

Suppose L   is the tangent line of y = 3 tan ⁡ x − 2 csc ⁡ x   at x = π 3 . Where does L   intersect the   x -axis?

选项
A.At x = 40 π 3
B.At  x = π 3 − 3 8
C.At x = π − 3 8
D.At x = 40 3
E.At x = 3 3 − 4 3
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标准答案
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思路分析
We begin by restating the problem in our own words to ensure we understand it: We have the function y = 3 tan x − 2 csc x, and L is the tangent line to this curve at x = π/3. We must find where this tangent line L intersects the x-axis (i.e., where y = 0). Now, step by step: 1) Compute the point of tangency (x0, y0) on the curve at x0 = π/3. - tan(π/3) = √3, so 3 tan x at x0 is 3√3. - csc(π/3) = 2/√3, so 2 csc x at x0 is 4/√3, and with the minus sign it becomes −4/√3. - Therefore y0 = 3 tan(π/3) − 2 csc(π/3) = 3√3 − 4/√3 = (9 − 4)/√3 = 5/√3. So the point of tangency......Login to view full explanation

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