zgunndashae zgunndashae
  • 21-02-2022
  • Mathematics
contestada

Find an equation of the tangent line to y = 2e^x sec(x) at x = pi/4

Respuesta :

zsm2800 zsm2800
  • 21-02-2022

Answer:

y = 6.20 + 12.4(x - pi/4)

Step-by-step explanation:

dy/dx = 2e^x secx + 2e^x secx * tanx= 2e^x secx (1 + tanx)

At x = pi/4, use sec(pi/4) = [tex]\sqrt{2}[/tex]. tan(pi/4) =1

so dy/dx = 2e^(pi/4) * [tex]\sqrt{2}[/tex] * (1 + 1) = [tex]4 \sqrt{2} e^{\pi/4}[/tex] ≈ 12.4 (This is the slope of the tangent line)

When x = pi/4, y =  2e^(pi/4) * [tex]\sqrt{2}[/tex]  = [tex]2 \sqrt{2} e^{\pi/4}[/tex]= 6.20

Then the equation of the tangent line is

y = 6.20 + 12.4(x - pi/4)

Answer Link

Otras preguntas

Anna can walk 10 miles in 4 hours. At this rate, how many minutes does it take her to walk one mile?
find the code word tyyy
Meredith went to visit her aunt over the weekend. It took her 1 1/2 hours to get there. If Meredith's aunt lived 96 miles away from Meredith's home, what was h
The following U.S. Treasury bond is listed in the The Wall Street Journal: Rate Mo/Yr Bid Asked 9.50 Oct 38 135:30 136:04 This $1,000 par value bond has 18 ye
why Shouldnt the Electoral College be Abolished?
Can an opposite and an absolute value of an integer be the same?
-3x + 10 < 28 what does x =
If every time production volume doubles, the direct labor costs decrease 20%, the learning curve is:
Which of the following types of soil has the greatest permeability? A. silty B. loam C. clay D. sandy
For a certain engineering project, how do we choose a design with the most favorable economic result?