Important Questions [19]
- Find the Stationary Points of the Function X3+3xy2-3x2-3y2+4 and Also Find Maximum and Minimum Values of the Function.
- Examine the Function F ( X , Y ) = X Y ( 3 − X − Y ) for Extreme Values and Find Maximum and Minimum Values of F ( X , Y ) .
- Find the Maxima and Minima of X 3 Y 2 ( 1 − X − Y )
- Find Maximum and Minimum Values of X3 +3xy2 -15x2-15y2+72x.
- If U = R 2 Cos 2 θ , V = R 2 Sin 2 θ . Find ∂ ( U , V ) ∂ ( R , θ )
- Prove that Tan 1 X = X − X 3 3 + X 5 5 + ... ... ... ... .
- Express ( 2 X 3 + 3 X 2 − 8 X + 7 ) in Terms of (X-2) Using Taylor'R Series.
- Expand 2 𝒙3 + 7 𝒙2 + 𝒙 – 6 in Power of (𝒙 – 2) by Using Taylors Theorem.
- Evaluate Lim X → 0 ( Cot X ) Sin X .
- Prove that Log [ Sin ( X + I Y ) Sin ( X − I Y ) ] = 2 Tan − 1 ( Cot X Tanh Y )
- P If sin 4 θ cos 3 θ = a cos θ + b cos 3 θ + o s 5 θ + d cos 7 θ then find a , b , c , d
- Expand Sec X by Mclaurin’S Theorem Considering up to X4 Term.
- Show that Sin ( E X − 1 ) = X 1 + X 2 2 − 5 X 4 24 + ...................
- Using Newton Raphson Method Solve 3x – Cosx – 1 = 0. Correct Upto 3 Decimal Places.
- Show that Xcosecx = 1 + X 2 6 + 7 X 4 360 + ... ...
- If Y= Cos (Msin_1 X).Prove that ( 1 − X 2 ) Y N + 2 − ( 2 N + 1 ) X Y N + 1 + ( M 2 − N 2 ) Y N = 0
- If Coshx = Secθ Prove that (I) X = Log(Secθ+Tanθ). (Ii) θ = π 2 Tan − 1 ( E − X )
- Prove that Cos − 1 Tanh ( Log X ) + = π – 2 ( X − X 3 3 + X 5 5 ... ... ... )
- If y = e 2 x sin x 2 cos x 2 sin 3 x . find y n
Concepts [7]
- Maxima and Minima of a Function of Two Independent Variables
- Jacobian
- Taylor’S Theorem (Statement Only)
- Taylor’S Series Method
- Maclaurin’s series (Statement only)
- Expansion of 𝑒^𝑥 , sin(x), cos(x), tan(x), sinh(x), cosh(x), tanh(x), log(1+x), 𝑠𝑖𝑛−1 (𝑥),𝑐𝑜𝑠−1 (𝑥),𝑡𝑎𝑛−1 (𝑥)
- Binomial Series
