Questions from General Calculus

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 - 2x, (0, 1)

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. sin x = x2 - x, (1, 2)

Q: a. Prove that the equation has at least one real root

a. Prove that the equation has at least one real root. b. Use your calculator to find an interval of length 0.01 that contains a root. cos x = x3

Q: a. Prove that the equation has at least one real root

a. Prove that the equation has at least one real root. b. Use your calculator to find an interval of length 0.01 that contains a root. ln x = 3 - 2x

Q: a. Prove that the equation has at least one real root

a. Prove that the equation has at least one real root. b. Use your graphing device to find the root correct to three decimal places. 100e-x/100 = 0.01x2

Q: Use a table of values to estimate the value of the limit

Use a table of values to estimate the value of the limit. If you have a graphing device, use it to confirm your result graphically.

Q: a. Prove that the equation has at least one real root

a. Prove that the equation has at least one real root. b. Use your graphing device to find the root correct to three decimal places. arctan x = 1 - x

Q: Prove, without graphing, that the graph of the function has

Prove, without graphing, that the graph of the function has at least two x­intercepts in the specified interval. y = sin x3, (1, 2)

Q: Prove, without graphing, that the graph of the function has

Prove, without graphing, that the graph of the function has at least two x­intercepts in the specified interval. y = x2 - 3 + 1/x, (0, 2)

Q: Prove that f is continuous at a if and only if

Prove that f is continuous at a if and only if