Tangent Slope at Point y=\cosh x = 1

  • Thread starter Thread starter bard
  • Start date Start date
  • Tags Tags
    Hyperbolic
AI Thread Summary
The discussion centers on finding the point on the curve y = cosh x where the tangent has a slope of 1. The user initially expresses uncertainty about how to approach the problem but later derives the relationship between the slope and the derivative, leading to the equation 1 = sinh x * dy/dx. By utilizing the definition of sinh, they ultimately determine that the solution occurs at x = ln(1 + √2). The conversation highlights the importance of understanding hyperbolic functions and their derivatives in solving such problems.
bard
Messages
65
Reaction score
0
at what point on the curve y=\cosh x does the tangent have slope 1


I have no idea how to approach this problem

my work

1=\sinh x\frac{dy}{dx}

\frac{1}{sinh x}=\frac{dy}{dx}
 
Physics news on Phys.org
It would probably help to you use the definitions.

For example:
\sinh{x}= \frac{e^{x}-e^{-x}}{2}
 
yah I found the answer as x=ln[1+sqt2]----thanks for your help
 
Thread 'Collision of a bullet on a rod-string system: query'
In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
Thread 'A cylinder connected to a hanged mass'
Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
Back
Top