Given a real valued function f of one variable (say x), the idea is to find an x such that (a)   ?

No spacing, write symbol if necessary.

A non-algebraic equation of trigonometric, exponential and logarithm function.

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(a)  

$$4x-3x^2y\ -15\ =\ 0$$   

What type of an equation?

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(a)  

The solution obtained by using analytical methods is called (a)   solution.

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The solution that obtained by using numerical methods is called (a)   solution.

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(a)   is the simplest method used in root finding.

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(a)   is a technique of calculating 𝑓(𝑥) for incremental values of 𝑥 over the interval where the root lies.

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It is referred as step size.

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(a)  

(a)   methods always converge to the true solution.

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Given f(x) = $$x^{2x}\ +\ \cos\ \left(x\right)-4$$   using bisection method. Use a stopping criterion below $$\in_s=0.5\%$$ . What is the value of $$x_u$$  .

Use numerical value (integer).

(a)  

Given f(x) = $$x^{2x}+\cos\left(x\right)-4$$     using bisection method. Use a stopping criterion below $$\in_s=0.50\%$$ . Determine the value of $$\in_a$$  .

Use numerical value (two decimal places).

Write 0 (prior to decimal point) and percent sign.

(a)  

Given f(x) = $$x^{2x}+\cos\left(x\right)-4$$       using bisection method. Use a stopping criterion below $$\in_s=0.5\%$$  .

Use integer for value of $$x_l$$  and $$x_u$$ .

Determine the $$x_r$$  in the 5th iteration. Use five decimal places.

(a)  

Given tan(πx)−6 = 0 in [0, 0.48], using the Method of False Position with stopping criterion of $$\in_s=0.5\%$$ . Determine the value of $$x_u$$ .

Write 0 prior to decimal point if necessary. Use two decimal places.

(a)  

Given tan(πx)−6 = 0 in [0, 0.48], using the Method of False Position with stopping criterion of $$\in_s=0.5\%$$ . Determine the value of $$f\left(x_l\right)$$  in the 8th iteration.

Write symbol if necessary. Use five decimal places.

(a)  

The idea of this method is to consider at least one initial guess which is not necessarily bracket the root.

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(a)  

It is an open method for finding roots of 𝑓(𝑥) = 0 by using the successive slope of the tangent line.

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(a)  

(a)   method that the derivative of a function is very difficult to find or even is not differentiable.

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This method is used finding the root of only those equations f(x) = 0 which are expressible as x = φ(x)

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(a)  

This is the oldest method of computing the real root of a numerical equation f(x) = 0 and it is almost a replica of bisection method.

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(a)  

Given f(x) = $$x^2$$  | sin(x) | - 4 using bisection method where x is in radian. Use a stopping criterion below $$\in_s=0.1\%$$ and an integer for lower and upper bound.

Determine the $$x_r$$  in the 5th iteration.

Use five decimal places.

(a)  

Given f(x) = $$x^2$$  | sin(x) | - 4 using bisection method where x is in radian. Use a stopping criterion below $$\in_s=0.1\%$$ and an integer for lower and upper bound.

Determine the $$\in_a$$   in the 4th iteration.

Use two decimal places and percent sign.

(a)  

Given y = 1 + 5.25x - sec ( $$\sqrt[]{0.68x}$$ ) by using incremental search method with stopping criterion below $$\in_s=2\%$$ . Use $$x_0=2.0$$ and h = 0.30.

Determine the $$\in_a$$ .

Use two decimal places and write percent sign.

(a)  

Given y = 1 + 5.25x - sec ( $$\sqrt[]{0.68x}$$ ) by using incremental search method with stopping criterion below $$\in_s=2\%$$ . Use $$x_0=2.0$$ and h = 0.30.

How many iterations required to find the root of the equation.

Use numerical value (integer).

(a)  

Given y = 1 + 5.25x - sec ( $$\sqrt[]{0.68x}$$ ) by using incremental search method with stopping criterion below $$\in_s=2\%$$ . Use $$x_0=2.0$$ and h = 0.30.

Determine the values of x in the first iteration where changed sign occurs.

Use this format $$\left[x_l,x_u\right]$$ .

Use two decimal places. No spacing.

(a)  

Given y = 1 + 5.25x - sec ( $$\sqrt[]{0.68x}$$ ) by using graphical method sets to $$0\le x\le2\pi$$   with stopping criterion below $$\in_s=2\%$$ .

Use $$x_0=2.0$$ and h = 0.30. Determine the solution/s.

Use numerical value.

(a)  

Given y = 1 + 5.25x - sec ( $$\sqrt[]{0.68x}$$ ) by using incremental search with stopping criterion below $$\in_s=2\%$$ .Use $$x_0=2.0$$ and h = 0.30.

Determine the $$x_r$$  in the first iteration.

Use two decimal places.

(a)  

Given tan(πx)−6 = 0 in [0, 0.48], using the Method of False Position with stopping criterion of $$\in_s=0.50\%$$ .Determine the $$\in_a$$  in the first iteration .

Use two decimal places and write percent sign if necessary.

(a)  

Given $$\cos\left(x^2\right)=0.5$$ by using graphical method sets $$0\le x\le\frac{3\pi}{2}$$ .

Determine the number solution/s.

Use an integer.

(a)  

Given $$\cos\left(x^2\right)=2$$ by using graphical method set x=0.

Determine the value of f(x).

(a)  

Given $$f\left(x\right)=x^3+0.5x^2-x$$  with $$x_{-1}=1$$  and $$x_0=3$$ by using secant method, find the $$\in_a$$  where i=2.

Use two decimal places and write the percent sign.

(a)  

Given $$f\left(x\right)=x^3+0.5x^2-x$$  with $$x_{-1}=1$$  and $$x_0=3$$ by using secant method, find the $$x_7$$ .

Use five decimal places and write 0 prior to decimal point.

(a)  

Determine the last iteration which $$f\left(x\right)=x^3+0.5x^2-x$$  with $$x_{-1}=1$$  and $$x_0=3$$ by using secant method.

Use numerical value (integer).

(a)  

Determine the upper bound of $$f\left(x\right)=\cos\left(x\right)-\sin\left(\frac{x}{2}\right)$$ .

Use an integer.

(a)  

Given $$f\left(x\right)=\cos\left(x\right)-\sin\left(\frac{x}{2}\right)$$  with $$x_0=8$$ .

Determine the $$f'\left(x_0\right)$$ .

Use five decimal places.

(a)  

Given $$f\left(x\right)=\cos\left(x\right)-\sin\left(\frac{x}{2}\right)$$  with $$x_0=8$$ using Newton Raphson method,

determine the $$\in_a$$ where $$x_i=3$$ .

Use two decimal places and write the percent sign.

(a)  

Perform five iterations using Newton Raphson method where $$f\left(x\right)=\cos\left(x\right)-\sin\left(\frac{x}{2}\right)$$  with $$x_0=8$$ , determine the $$x_4$$  .

Use five decimal places.

(a)  

Using Newton Raphson method where $$f\left(x\right)=\cos\left(x\right)-\sin\left(\frac{x}{2}\right)$$  with $$x_0=8$$ , determine the $$x_{i+1}$$  where i=2.

Use five decimal places.

(a)  

Given $$f\left(x\right)=\cos\left(x\right)+\sin\left(x\right)-1$$ by using graphical method, determine the $$x_l$$ . Use an integer.

(a)  

(a)   method is used to find an approximate root in an interval by repeatedly bisecting into subintervals.

Use small letter.