4.A] EvaluateΒ
(i) lim π₯β0Β (ππ₯ + π₯)1/π₯Β Β Β Β Β Β Β Β Β Β Β Β Β Β (ii) lim π₯Β π βπ/2 (tan π₯)tan2π₯
Category 21mat11
If π’ = π¦π§/x, π£ = π§π₯/y, π€ = π₯π¦/z, show thatΒ π(π’,π£,π€)/π(π₯.π¦,π§)Β = 4
If π’ = π¦π§/x, π£ = π§π₯/y, π€ = π₯π¦/z, show thatΒ π(π’,π£,π€)/π(π₯.π¦,π§)Β = 4
If π’ = π‘ππβ1 (π¦/π₯) ,π€βπππ π₯ = ππ‘ β πβπ‘πππ π¦ = ππ‘ + πβπ‘, find the total derivative (ππ’/ππ‘) using partial differentiation.
If π’ = π‘ππβ1 (π¦/π₯) ,π€βπππ π₯ = ππ‘ β πβπ‘πππ π¦ = ππ‘ + πβπ‘, find the total derivative (ππ’/ππ‘) using partial differentiation. Answer:-
Expand β1 + π ππ2π₯ by Maclaurinβs series up to the term containing π₯5
3.A. Expand β1 + π ππ2π₯ by Maclaurinβs series up to the term containing π₯5
Show that the radius of curvature at (π,0) on the curve π^π =π^π(πβπ) / π is π π
2. C) Show that the radius of curvature at (π,0) on the curve ππΒ = ππ(πβπ) / π is π/2 Answer:-
Find the pedal equation of the curve ππ = ππ cos ππ
2. B) Find the pedal equation of the curve ππ = ππ cos ππ. Answer:-
Show that the curves π^π = π^π cos ππ and π^π = π^π sin ππ cut orthogonally.
2. A) Show that the curves ππ = ππ cos ππ and ππ = ππ sin ππ cut each other orthogonally. Answer:-
Prove that for the cardioids π = π(1 + cos π), π2/r is constant
C) Prove that for the cardioids π = π(1 + cos π), π2/r is constant Answer:-
Find the angle between the curves π = π ππππ and π = π/ππππ
1.B) Find the angle between the curves π = π ππππ and π = π/ππππ
With usual notations prove π =(1+π¦1^2 )^3/2 / y2
1.A] With usual notations prove that π =(1+π¦1 2 ) 3/2/y2