Questions from General Calculus

Q: A hyperbola never intersects its directrix.

A hyperbola never intersects its directrix.

Q: The function f(x) = (ln x)/x

The function f(x) = (ln x)/x is a solution of the differential equation x2y’ + xy = 1.

Q: If y is the solution of the initial-value problem

If y is the solution of the initial-value problem

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

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

Q: First make a substitution and then use integration by parts to evaluate

First make a substitution and then use integration by parts to evaluate the integral.

Q: The Midpoint Rule is always more accurate than the Trapezoidal Rule.

The Midpoint Rule is always more accurate than the Trapezoidal Rule.

Q: Find the Maclaurin series of f (by any method) and

Find the Maclaurin series of f (by any method) and its radius of convergence. Graph f and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these p...

Q: Determine whether the sequence converges or diverges. If it converges,

Determine whether the sequence converges or diverges. If it converges, find the limit.

Q: (a) Every elementary function has an elementary derivative.

(a) Every elementary function has an elementary derivative. (b) Every elementary function has an elementary antiderivative.

Q: Use a graphing device (or the interactive graphic in TEC Module

Use a graphing device (or the interactive graphic in TEC Module 10.1B) to draw the graphs of hypocycloids with a positive integer and b = 1. How does the value of a affect the graph? Show that if we t...