Questions from Calculus

Q: Prove that if / = 0 and │g(x)│≤

Prove that if / = 0 and │g(x)│≤ M for a fixed number M and all x ≠ c, then / [ f(x)g(x)] = 0.

Q: a. Prove that if /│f(x)│ = 0

a. Prove that if /│f(x)│ = 0 then /f(x) =0 b. Prove that if / f(x) = L, then / │ f(x)│ = │L│. [Hint: Use the inequality ││f(x)│ − │L││ ≤ │ f(x) − L│.]

Q: Use the graph shown in the figure. /

Use the graph shown in the figure. Identify or sketch each of the quantities on the figure. a. f(1) and f(4) b. f(4) − f(1) c. 4 – 1 d. /

Q: (a) Find an equation of the tangent line to the

(a) Find an equation of the tangent line to the graph of f at the given point, (b) use a graphing utility to graph the function and its tangent line at the point, and (c) use the tangent feature of a...

Q: Find a function f to show that the converse of Exercise 112

Find a function f to show that the converse of Exercise 112 (b) is not true. [Hint: Find a function f such that / │ f(x)│ = │L│ but / f(x) does not exist.]

Q: When using a graphing utility to generate a table to approximate

When using a graphing utility to generate a table to approximate a student concluded that the limit was 0.01745 rather than 1. Determine the probable cause of the error.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f(x) = g(x) for all real numbers other than x = 0 and

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.