Question

find center of curvature of curve y=log(secx) at (π/3, log 2) ​

Answer 1

Answer:

curve y=log secx between the points x = 0 and x. = π/3 is log(2+ √3). Solution ... Differentiating (1) w.r.t x, we get:.

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Answer 2

Given: curve y=log(secx)

To find: Center of curvature of the curve at (π/3, log 2)

Solution: The radius of curvature of any function is given by a formula

R = y"/ ( 1+y'^2)^3/2

here y' is the first derivative and y""is the second derivative of the function.

So given function is

y= log(secx)

y' = secxtanx/secx = tanx

y"= (secx)^2

on putting values in the formula of the radius of curvature we get

R = (secx)^2/ (1+(tanx)^2)^3/2

we need to find the radius of curvature at a point (π/3, log 2) on the curve

R= 4/(1+3)^3/2 = 4/4^3/2 = 1/√4 = 1/2

Therefore, the radius of curvature of curve y=log(secx) at (π/3, log 2) is 1/2.