Questions from General Calculus

Q: a. Use a graph to find a number such that

a. Use a graph to find a number such that if 2 < x < 2 + δ then 1/ln(x – 1) > 100 b. What limit does part (a) suggest is true?

Q: Given that limx →π csc2 x = ∞, illustrate Definition 6

Given that limx →π csc2 x = ∞, illustrate Definition 6 by finding values of that correspond to a. M = 500 and b. M = 1000.

Q: A machinist is required to manufacture a circular metal disk with area

A machinist is required to manufacture a circular metal disk with area 1000 cm2. a. What radius produces such a disk? b. If the machinist is allowed an error tolerance of (5 cm2 in the area of the d...

Q: A crystal growth furnace is used in research to determine how best

A crystal growth furnace is used in research to determine how best to manufacture crystals used in electronic components for the space shuttle. For proper growth of the crystal, the temperature must b...

Q: a. Find a number δ such that if |x -

a. Find a number δ such that if |x - 2| < δ, then |4x - 8|< ε, where ε = 0.1. b. Repeat part (a) with ε = 0.01.

Q: Given that limx → 2 (5x – 7) = 3

Given that limx → 2 (5x – 7) = 3, illustrate Definition 2 by finding values of  that correspond to ε = 0.1, ε = 0.05, and ε = 0.01.

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. f(x) = x2 + x / x3 + x2

Q: Prove the statement using the ε, δ  definition of a

Prove the statement using the ε, δ definition of a limit and illustrate with a diagram like Figure 9. From Figure 9

Q: Prove the statement using the ε, δ  definition of a

Prove the statement using the ε, δ definition of a limit and illustrate with a diagram like Figure 9. From Figure 9

Q: Prove the statement using the ε, δ  definition of a

Prove the statement using the ε, δ definition of a limit and illustrate with a diagram like Figure 9. From Figure 9