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Find maximum and minimum values of x3 +3xy2 -15x2-15y2+72x.
Concept: Maxima and Minima of a Function of Two Independent Variables
Expand 2 𝒙3 + 7 𝒙2 + 𝒙 – 6 in power of (𝒙 – 2) by using Taylors Theorem.
Concept: Taylor’S Series Method
Expand sec x by McLaurin’s theorem considering up to x4 term.
Concept: 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)
Evaluat `lim_(x->0) (e^(2x)-(1+x)^2)/(xlog(1+x)`
Concept: L‐ Hospital Rule
Solve the following equation by Gauss-Seidel method upto four iterations
4x-2y-z=40, x-6y+2y=-28, x-2y+12z=-86.
Concept: Gauss Seidal Iteration Method
Solve the following system of equation by Gauss Siedal Method,20x+y-2z=17
3x+20y-z =-18
2x-3y+20z=𝟐𝟓
Concept: Gauss Seidal Iteration Method
Find the roots of the equation `x^4+x^3 -7x^2-x+5 = 0` which lies between 2 and 2.1 correct to 3 places of decimals using Regula Falsi method.
Concept: Regula – Falsi Equation
Evaluate : `lim_(x->0)((2x+1)/(x+1))^(1/x)`
Concept: L‐ Hospital Rule
Solve the following equation by Gauss Seidal method:
`10x_1+x_2+x_3=12`
`2x_1+10x_2+x_3-13`
`2x_1+2x_2+10x_3=14`
Concept: Gauss Seidal Iteration Method
Obtain the root of 𝒙𝟑−𝒙−𝟏=𝟎 by Regula Falsi Method
(Take three iteration).
Concept: Regula – Falsi Equation
Solve by Gauss Jacobi Iteration Method: 5x – y + z = 10, 2x + 4y = 12, x + y + 5z = -1.
Concept: Gauss Jacobi Iteration Method
By using Regular falsi method solve 2x – 3sin x – 5 = 0.
Concept: Regula – Falsi Equation
Solve using Gauss Jacobi Iteration method
2𝒙 + 12y + z – 4w = 13
13𝒙 + 5y - 3z + w = 18
2𝒙 + y – 3z + 9w = 31
3𝒙 - 4y + 10z + w = 29
Concept: Gauss Jacobi Iteration Method
