Question

find the radius of curvature y = cosh (x/c) at (0,c)​

Answer 1

Answer:

c

Step-by-step explanation:

y1=sinh(x/c)

y2=1/c cosh(x/c)

point at (0,c)

y1=0

y2=1/c

apply in formula,we get

radius of curvature=(1+y1^2)^3/2÷y2

therefore we get,

solution is. c

Answer 2

The radius of curvature of the curve y = cosh(x/c) at the point (0, c) is $c^2$.

To find the radius of curvature of the curve y = cosh(x/c) at the point (0, c), we need to use the following formula:

r = $[(1 + y'^2)^(3/2)] / |y"|$

where y' and y" denote the first and second derivatives of y with respect to x, respectively.

Let's start by determining y's first derivative:

y' = sinh(x/c) / c

At the point (0, c), y' = sinh(0/c) / c = 0/c = 0.

Next, let's find the second derivative of y:

y" =$cosh(x/c) / c^2$

At the point (0, c), y" = $cosh(0/c) / c^2 = 1 / c^2.$

Now, we can plug in y' and y" into the formula for the radius of curvature:

r =$[(1 + y'^2)^(3/2)] / |y"|$

= $[(1 + 0^2)^(3/2)] / |1 / c^2|$

= $c^2$

Therefore, the radius of curvature of the curve y = cosh(x/c) at the point (0, c) is $c^2$.

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