Questions from General Calculus

Q: If / then the root of the equation f (

If then the root of the equation f (x) = 0 is x = 0. Explain why Newton’s method fails to find the root no matter which initial approximation x1 ≠ 0 is used. Illust...

Q: (a) Use Newton’s method to find the critical numbers of

(a) Use Newton’s method to find the critical numbers of the function f (x) = x6 - x4 + 3x3 - 2x correct to six decimal places. (b) Find the absolute minimum value of f correct to four decimal places....

Q: Differentiate the function. g(t) = 2t-

Differentiate the function. g(t) = 2t-3/4

Q: Use Newton’s method to find the absolute maximum value of the function

Use Newton’s method to find the absolute maximum value of the function f (x) = x cos x, 0 ≤ x ≤ π, correct to six decimal places.

Q: Use Newton’s method to find the coordinates of the inflection point of

Use Newton’s method to find the coordinates of the inflection point of the curve y = x2 sin x, 0 ≤ x ≤ π, correct to six decimal places.

Q: Of the infinitely many lines that are tangent to the curve y

Of the infinitely many lines that are tangent to the curve y = 2sin x and pass through the origin, there is one that has the largest slope. Use Newton’s method to find the slope of that line correct t...

Q: Use Newton’s method to find the coordinates, correct to six decimal

Use Newton’s method to find the coordinates, correct to six decimal places, of the point on the parabola y = (x – 1)2 that is closest to the origin.

Q: In the figure, the length of the chord AB is 4

In the figure, the length of the chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle θ, in radians, correct to four decimal places. Then give the answer to the n...

Q: The figure shows the sun located at the origin and the earth

The figure shows the sun located at the origin and the earth at the point (1, 0). (The unit here is the distance between the centers of the earth and the sun, called an astronomical unit: 1 AU ≈ 1.496...

Q: The figure shows the graph of a function f. Suppose that

The figure shows the graph of a function f. Suppose that Newton’s method is used to approximate the root s of the equation f (x) = 0 with initial approximation x1 = 6. (a) Draw the t...