Given x = t + t<sup>–1</sup> and y = t – t<sup>–1</sup> the value of dy/dx at t = 2 is

EXERCISE 8 A Q. 25
Q.25) Given x = t + t^–1 and y = t – t^–1 the value of dy/dx at t = 2 is

Try again

Correct

Try again

x = t + t^–1
Diff.w.r.t.t, we get
dx/dt = 1 + (-1/t²)
dx/dt = (t² - 1 )/ t²
and y = t – t^–1
Diff.w.r.t. t we get,
dy/dt = 1 - (-1 /t²
dy /dt = (t² + 1 )/ t²
Now dy/dx = (dy/dt)/(dx/dt)
dy/dx = (t² + 1 )/ (t² - 1 )
dy/dx at t=2 = (4+1)/(4 - 1)
dy/dx = 5/3
Answer : (c)

Study Companion