Questions from General Calculus

Q: (a). If the symbol [[]] denotes the greatest integer function

(a). If the symbol [[]] denotes the greatest integer function defined in Example 9, evaluate (b). If n is an integer, evaluate (c). For what values of does limx→a [x] exist?

Q: From the graph of f, state the intervals on which is

From the graph of f, state the intervals on which is continuous.

Q: Use the graph of the function f to state the value of

Use the graph of the function f to state the value of each limit, if it exists. If it does not exist, explain why.

Q: In the theory of relativity, the Lorentz contraction formula expresses the

In the theory of relativity, the Lorentz contraction formula expresses the length L of an object as a function of its velocity v with respect to an observer, where l0 is the length of the object at re...

Q: If p is a polynomial, show that limv→a P

If p is a polynomial, show that limv→a P (x) = P (a).

Q: If a rock is thrown upward on the planet Mars with a

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after seconds is given by H = 10t – 1.86t2. (a). Find the velocity of the rock after one second. (b). Fi...

Q: If r is a rational function, use Exercise 43 to show

If r is a rational function, use Exercise 43 to show that limv→a r (x) = r (a) for every number a in the domain of r. Exercise 43: If p is a polynomial, show that limv→a P (x) = P (a).

Q: If limx→1 f (x) – 8/x

If limx→1 f (x) – 8/x-1 = 10, find limx→1 f (x).

Q: Sketch the graph of a function that is continuous except for the

Sketch the graph of a function that is continuous except for the stated discontinuity. Discontinuous, but continuous from the right, at 2

Q: Prove that cosine is a continuous function.

Prove that cosine is a continuous function.