Solve dy/dx+ y tan x = y^3sec x
5. A) Solve dy/dx+ y tan x = y3sec x Answer:-
Category solved model papers
Find the extreme values of x3+y3-3axy , a>=0
4. C) Find the extreme values of x3+y3-3axy , a>=0
If u = f(y-x/xy, z-x/xz), show that x² ∂u/∂x + y2 ∂
If u = f(y-x/xy, z-x/xz), show that x² ∂u/∂x + y2 ∂
4.A] Evaluate
(i) lim 𝑥→0 (𝑎𝑥 + 𝑥)1/𝑥 (ii) lim 𝑥 𝜋 →𝜋/2 (tan 𝑥)tan2𝑥
If 𝑢 = 𝑦𝑧/x, 𝑣 = 𝑧𝑥/y, 𝑤 = 𝑥𝑦/z, show that 𝛛(𝑢,𝑣,𝑤)/𝛛(𝑥.𝑦,𝑧) = 4
If 𝑢 = 𝑦𝑧/x, 𝑣 = 𝑧𝑥/y, 𝑤 = 𝑥𝑦/z, show that 𝛛(𝑢,𝑣,𝑤)/𝛛(𝑥.𝑦,𝑧) = 4
If 𝑢 = 𝑡𝑎𝑛−1 (𝑦/𝑥) ,𝑤ℎ𝑒𝑟𝑒 𝑥 = 𝑒𝑡 − 𝑒−𝑡𝑎𝑛𝑑 𝑦 = 𝑒𝑡 + 𝑒−𝑡, find the total derivative (𝑑𝑢/𝑑𝑡) using partial differentiation.
If 𝑢 = 𝑡𝑎𝑛−1 (𝑦/𝑥) ,𝑤ℎ𝑒𝑟𝑒 𝑥 = 𝑒𝑡 − 𝑒−𝑡𝑎𝑛𝑑 𝑦 = 𝑒𝑡 + 𝑒−𝑡, find the total derivative (𝑑𝑢/𝑑𝑡) using partial differentiation. Answer:-
Expand √1 + 𝑠𝑖𝑛2𝑥 by Maclaurin’s series up to the term containing 𝑥5
3.A. Expand √1 + 𝑠𝑖𝑛2𝑥 by Maclaurin’s series up to the term containing 𝑥5
Show that the radius of curvature at (𝑎,0) on the curve 𝒚^𝟐 =𝒂^𝟐(𝒂−𝒙) / 𝒙 is 𝒂 𝟐
2. C) Show that the radius of curvature at (𝑎,0) on the curve 𝒚𝟐 = 𝒂𝟐(𝒂−𝒙) / 𝒙 is 𝒂/2 Answer:-
Find the pedal equation of the curve 𝑟𝑛 = 𝑎𝑛 cos 𝑛𝜃
2. B) Find the pedal equation of the curve 𝑟𝑛 = 𝑎𝑛 cos 𝑛𝜃. Answer:-
Show that the curves 𝑟^𝑛 = 𝑎^𝑛 cos 𝑛𝜃 and 𝑟^𝑛 = 𝑏^𝑛 sin 𝑛𝜃 cut orthogonally.
2. A) Show that the curves 𝑟𝑛 = 𝑎𝑛 cos 𝑛𝜃 and 𝑟𝑛 = 𝑏𝑛 sin 𝑛𝜃 cut each other orthogonally. Answer:-