Questions from General Calculus

Q: Let / a. Evaluate each of the

Let a. Evaluate each of the following, if it exists. b. Sketch the graph of t.

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

a. If the symbol [[ ]] denotes the greatest integer function defined in Example 10, evaluate b. If n is an integer, evaluate c. For what values of a does limx → a [[x]] exist?

Q: Let f(x) = [[cos x]], -π

Let f(x) = [[cos x]], -π ≤ x ≤ π . a. Sketch the graph off. b. Evaluate each limit, if it exists. c. For what values of a does limx &a...

Q: If f(x) = [[x]] + [[2x

If f(x) = [[x]] + [[2x]], show that limx→2 f(x) exists but is not equal to f(2).

Q: Sketch the graph of the function and use it to determine the

Sketch the graph of the function and use it to determine the values of a for which limx → a f(x) exists.

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

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...

Q: If p is a polynomial, show that lim x→a

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

Q: If r is a rational function, use Exercise 57 to show

If r is a rational function, use Exercise 57 to show that limx→a r(x) = r(a) for every number a in the domain of r.

Q: If / f(x) – 8/x - 1

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

Q: If / f(x) x2 = 5, find the

If / f(x) x2 = 5, find the following limits.