Questions from General Calculus

Q: To prove that sine is continuous, we need to show that

To prove that sine is continuous, we need to show that limx→a sinx = sina for every real number a. By Exercise 63 an equivalent statement is that Use (6) to show that t...

Q: Prove that cosine is a continuous function.

Prove that cosine is a continuous function.

Q: a. Prove Theorem 4, part 3. b.

a. Prove Theorem 4, part 3. b. Prove Theorem 4, part 5.

Q: For what values of x is f continuous? /

For what values of x is f continuous?

Q: For what values of x is g continuous? /

For what values of x is g continuous?

Q: Is there a number that is exactly 1 more than its cube

Is there a number that is exactly 1 more than its cube?

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: If a and b are positive numbers, prove that the equation

If a and b are positive numbers, prove that the equation a/ x3 + 2x2 – 1 + b/ x3 + x - 2 = 0 has at least one solution in the interval (-1, 1).

Q: Show that the function / is continuous on

Show that the function is continuous on (-∞, ∞)

Q: a. Show that the absolute value function F(x)

a. Show that the absolute value function F(x) = |x| is continuous everywhere. b. Prove that if f is a continuous function on an interval, then so is | f |. c. Is the converse of the statement in par...