Questions from General Calculus

Q: Find the horizontal and vertical asymptotes of each curve. If you

Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes.

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

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

Q: Find the horizontal and vertical asymptotes of each curve. If you

Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes.

Q: (a). Use a graph of f (x) =

(a). Use a graph of f (x) = √3x2 + 8x + 6 – 3x2 + 3x + 1 to estimate the value of limx→∞ f (x) to one decimal place. (b). Use a table of values of f (x) to estimate the limit to four decimal places. (...

Q: Estimate the horizontal asymptote of the function f (x) =

Estimate the horizontal asymptote of the function f (x) = 3x2 + 500 x2/ x2 + 500 x2 + 100x + 2000 by graphing f for -10 < x < 10. Then calculate the equation of the asymptote by evaluating the limit....

Q: If limx→1 f (x)/x2 = 5 find

If limx→1 f (x)/x2 = 5 find the following limits. (a). limx→0 f (x) (b). limx→0 f (x)/x

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

To prove that sine is continuous we need to show that limx→a sin x = sin a for every real number a. If we let h = x - a, then x = a + h and x→a ⇔ h → 0. So, an equivalent statement is that limh→a sin...

Q: Sketch the graph of an example of a function f that satisfies

Sketch the graph of an example of a function f that satisfies all of the given conditions.

Q: Sketch the graph of an example of a function f that satisfies

Sketch the graph of an example of a function f that satisfies all of the given conditions.

Q: Find limx→∞ f (x) if, for all x

Find limx→∞ f (x) if, for all x > 1,