Virtual Labs

Convergence and computation time

Bisection method is

a: direct method Explanation

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b: one point iterative method Explanation

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c: fix point iterative method Explanation

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d: bracketing method Explanation

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If f(x₁) × f(x₂) < 0, select most suitable option.

a: x₁ & x₂, contains root Explanation

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b: x₁ & x₂, contains at least one root Explanation

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c: x₁ & x₂, contains multiple roots Explanation

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d: x₁ & x₂,contains only real roots Explanation

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If f(x₁) × f(x₂) > 0, select most suitable option.

a: Root lies between x₁ & x₂ Explanation

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b: Root does not lie between x₁ & x₂ Explanation

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c: Root may lie or may not lie between x₁ & x₂ Explanation

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d: Root does not exsists Explanation

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If f(x₁) × f(x₂) = 0

a: Equation do not have real root Explanation

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b: Equation do not have root Explanation

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c: Either x₁ or x₂ is the root of the equation Explanation

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d: Equation cannot be solved by bisection method Explanation

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False position method is

a: direct method Explanation

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b: bracketing method Explanation

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c: fix point iterative method Explanation

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d: one point iterative method Explanation

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If f(x₁) × f(x₂) < 0, select most suitable option.

a: x₁ & x₂, contains at least one root Explanation

Explanation

b: x₁ & x₂, contains root Explanation

Explanation

c: x₁ & x₂, contains multiple roots Explanation

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d: x₁ & x₂,contains only real roots Explanation

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If f(x₁) × f(x₂) > 0, select most suitable option.

a: Root lies between x₁ & x₂ Explanation

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b: Root does not lie between x₁ & x₂ Explanation

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c: Root may lie or may not lie between x₁ & x₂ Explanation

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d: Root does not exsists Explanation

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If f(x₁) × f(x₂) = 0

a: Either x₁ or x₂ is the root of the equation Explanation

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b: Equation do not have real root Explanation

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c: Equation do not have root Explanation

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d: Equation cannot be solved by false position method Explanation

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If the convergence criteria is not satisfied

a: then you will not get the root of the equation Explanation

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b: you may or may not get the root of the equation Explanation

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c: Explanation

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d: Explanation

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Newton raphson is a

a: bracketing method Explanation

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b: open method Explanation

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c: Explanation

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d: Explanation

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New improved approximation of root is given by

x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}

Explanation

x_2 = g(x)

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x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}, \quad f'(x_1) → \text{at only first guess} \

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x_2 = x_1 - \frac{f'(x_1)}{f(x_1)}

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If the convergence criteria is not satisfied

a: you may or may not get the root of the equation Explanation

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b: then you will not get the root of the equation Explanation

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c: Explanation

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d: Explanation

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Newton raphson is a

a: bracketing method Explanation

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b: open method Explanation

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c: Explanation

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d: Explanation

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New improved approximation of root is given by

x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}

Explanation

x_2 = g(x)

Explanation

x_2 = x_1 - \frac{f(x_1)}{f'(x_1)}, \quad f'(x_1) → \text{at only first guess} \

Explanation

x_2 = x_1 - \frac{f'(x_1)}{f(x_1)}

Explanation