Questions from General Calculus

Q: Consider the following problem: Find two numbers whose sum is 23

Consider the following problem: Find two numbers whose sum is 23 and whose product is a maximum. (a) Make a table of values, like the one at the right, so that the sum of the numbers in the first two...

Q: Use Newton’s method to approximate the given number correct to eight decimal

Use Newton’s method to approximate the given number correct to eight decimal places. 4 75

Q: Find two numbers whose difference is 100 and whose product is a

Find two numbers whose difference is 100 and whose product is a minimum.

Q: Use Newton’s method to approximate the given number correct to eight decimal

Use Newton’s method to approximate the given number correct to eight decimal places. 8 500

Q: Find two positive numbers whose product is 100 and whose sum is

Find two positive numbers whose product is 100 and whose sum is a minimum.

Q: (a) Explain how we know that the given equation must

(a) Explain how we know that the given equation must have a root in the given interval. (b) Use Newton’s method to approximate the root correct to six decimal places. 3x4 - 8x3 + 2 = 0, [2, 3]

Q: The sum of two positive numbers is 16. What is the

The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?

Q: (a) Explain how we know that the given equation must

(a) Explain how we know that the given equation must have a root in the given interval. (b) Use Newton’s method to approximate the root correct to six decimal places. -2x5 + 9x4 - 7x3 - 11x = 0, [3, 4...

Q: What is the maximum vertical distance between the line y = x

What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for --1 ≤ x ≤ 2?

Q: Use Newton’s method to approximate the indicated root of the equation correct

Use Newton’s method to approximate the indicated root of the equation correct to six decimal places. The negative root of ex = 4 - x2