Question

If $k \ge 1$, the graphs of $y = \sin x$ and $y = ke^{-x}$ intersect for $x \ge 0$. Find the smallest value of $k$ for which the graphs are tangent. $k = \text{___}$ What are the coordinates of the point of tangency? $x = \text{_}, y = \text{___}$

Name: if k ge 1 the graphs of y sin x and y ke x intersect for x ge 0 find the smallest value of k for which the graphs are tangent k text what are the coordinates of the point of tangency x 79275
Uploaded: 2024-10-21T08:13:53-08:00
Duration: 2 min 11 s
Channel: Shu Naito
Description: if k ge 1 the graphs of y sin x and y ke x intersect for x ge 0 find the smallest value of k for which the graphs are tangent k text what are the coordinates of the point of tangency x 79275

          If $k \ge 1$, the graphs of $y = \sin x$ and $y = ke^{-x}$ intersect for $x \ge 0$. Find the smallest value of $k$ for which the graphs are tangent.
$k = \text{_____}$
What are the coordinates of the point of tangency?
$x = \text{_____}, y = \text{_____}$

if k ge 1 the graphs of y sin x and y ke x intersect for x ge 0 find the smallest value of k for which the graphs are tangent k text what are the coordinates of the point of tangency x 79275

Added by Donna P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shu Naito

10/21/2024

Step 1

If the graphs are tangent, then $y_1 = y_2$ and $y_1' = y_2'$ at the point of tangency. $y_1' = \cos x$ and $y_2' = -ke^{-x}$. Thus, we have the equations: $\sin x = ke^{-x}$ (1) $\cos x = -ke^{-x}$ (2) Show more…

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If $k \ge 1$, the graphs of $y = \sin x$ and $y = ke^{-x}$ intersect for $x \ge 0$. Find the smallest value of $k$ for which the graphs are tangent. $k = \text{_____}$ What are the coordinates of the point of tangency? $x = \text{_____}, y = \text{_____}$