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Q. Show that the following curves are unit–speed:
(i) γ(t) = (1/3 〖(1+t)〗^(3/2),1/3 〖(1-t)〗^(3/2),t/√2 )
(ii) γ(t) = (4/5 cost,1-sint,-3/5 cost)
(i) γ(t) = (1/3 〖(1+t)〗^(3/2),1/3 〖(1-t)〗^(3/2),t/√2 )
(ii) γ(t) = (4/5 cost,1-sint,-3/5 cost)
Q. Calculate the arc–length of catenary γ(t) = (t, cosh t) starting at the point (0, 1).
Q. Calculate the arc length of catenary γ(t) = (t, cosh t) starting at the point (0, 1).
Q. Calculate the tangent vectors of the following curves:
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
Q. Find the cartesian equations of following parametrized curves:
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
(i) γ(t) = (cos^2 t, sin^2 t)
(ii) γ(t) = (e^t, t^2)
Q.Find the length of the astroid x=acos^3 t, y=asin^3 t, [0, 2π].
Q. Find parametrisations of following level curves
Y^2-x^2=1, x^2/4+y^2/9 =1
Y^2-x^2=1, x^2/4+y^2/9 =1
Q. Find parametrisations of following level curves
Y^2-x^2=1, x^2/4+y^2/9 =1
Y^2-x^2=1, x^2/4+y^2/9 =1
Q. Is γ(t) = (t2, t4) a parameterization of the parabola y=x2?
Construct a 90% confidence interval for the proportion of smokers who quit smoking by using either the patch or e-cigarettes within 6 months
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#333702 on Dec 2022
#333702 on Dec 2022