Questions from General Calculus

Q: Determine if the given expression approaches a limit as b → ∞,

Determine if the given expression approaches a limit as b → ∞, and find that number when it does. 2 - (b + 1)-1/2

Q: State the formula for the integration by parts of a definite integral

State the formula for the integration by parts of a definite integral.

Q: State the midpoint rule. (Include the meaning of all symbols

State the midpoint rule. (Include the meaning of all symbols used.)

Q: State the trapezoidal rule. (Include the meaning of all symbols

State the trapezoidal rule. (Include the meaning of all symbols used.)

Q: Explain the formula S = (2M + T)/3.

Explain the formula S = (2M + T)/3.

Q: State the error of approximation theorem for each of the three approximation

State the error of approximation theorem for each of the three approximation rules.

Q: Determine the integrals by making appropriate substitutions. ∫ ln(

Determine the integrals by making appropriate substitutions. ∫ ln(3x) /3x dx

Q: State the formula for each of the following quantities: (

State the formula for each of the following quantities: (a) Present value of a continuous stream of income (b) Total population in a ring around the center of a city

Q: How do you determine whether an improper integral is convergent?

How do you determine whether an improper integral is convergent?

Q: Describe integration by substitution in your own words.

Describe integration by substitution in your own words.