Questions from General Calculus

Q: Explain, using Theorems 4, 5, 7, and 9

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain.

Q: Explain, using Theorems 4, 5, 7, and 9

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. G (t) = ln (t4 – 1)

Q: Explain, using Theorems 4, 5, 7, and 9

Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. F (x) = sin (cos (sin x))

Q: Shown are graphs of the position functions of two runners, A

Shown are graphs of the position functions of two runners, A and B, who run a 100-m race and finish in a tie. (a). Describe and compare how the runners run the race. (b). At what time is the distanc...

Q: Locate the discontinuities of the function and illustrate by graphing.

Locate the discontinuities of the function and illustrate by graphing. y = 1/1 + e1/x

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

(a). Use a graph of f (x) = √3 + x - √3/x to estimate the value of limx→0 f (x) to two decimal places. (b). Use a table of values of f (x) to estimate the limit to four decimal places. (c). Use the Li...

Q: Use the Squeeze Theorem to show that limx→0 (x2

Use the Squeeze Theorem to show that limx→0 (x2 cos 20πx) = 0. Illustrate by graphing the functions f (x) = -x2, g (x) = x2 cos 20πx, and h (x) = x2 on the same screen.

Q: Use continuity to evaluate the limit. limx→π sin

Use continuity to evaluate the limit. limx→π sin (x + sin x)

Q: Use continuity to evaluate the limit. limx→π ex2

Use continuity to evaluate the limit. limx→π ex2-x

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).