Questions from General Calculus

Q: (a). Estimate the value of limx→0 x/

(a). Estimate the value of limx→0 x/ 1 + 3x – 1 by graphing the function f (x) = x/ (√1 + 3x – 1). (b). Make a table of values of f (x) for x close to 0 and guess the value of the limit. (c). Use the...

Q: Use the Squeeze Theorem to show that limx→0 √x3

Use the Squeeze Theorem to show that limx→0 √x3 + x2 sin π/x = 0 Illustrate by graphing the functions f, g and h (in the notation of the Squeeze Theorem) on the same screen.

Q: If 4x – 9 < f (x) < x2 –

If 4x – 9 < f (x) < x2 – 4x + 7 for x > 0, find limx→4 f (x).

Q: If 2x < g (x) < x4 – x2 +

If 2x < g (x) < x4 – x2 + 2 for all x, evaluate limx→1 g (x).

Q: Prove that limx→0+ √x esinπ/x =

Prove that limx→0+ √x esinπ/x = 0.

Q: Find the limit, if it exists. If the limit does

Find the limit, if it exists. If the limit does not exist, explain why.

Q: Let F (x) = x2 – 1/|x –

Let F (x) = x2 – 1/|x – 1|. (a) Find (i). limx→1+ F (x) (ii). limx→1- F (x) (b). Does limx→1 F (x) exist? (c). Sketch the graph of F.

Q: Evaluate the limit and justify each step by indicating the appropriate Limit

Evaluate the limit and justify each step by indicating the appropriate Limit Law(s).  

Q: The turkey in Example 1 is removed from the oven when its

The turkey in Example 1 is removed from the oven when its temperature reaches 1850F and is placed on a table in a room where the temperature is 750F. After 10 minutes the temperature of the turkey is...

Q: If a ball is thrown vertically upward with a velocity of 80

If a ball is thrown vertically upward with a velocity of 80 ft/s, then its height after seconds is s = 80t – 16t2. (a). What is the maximum height reached by the ball? (b). What is the velocity of the...