Theories, Problems, Solutions

Cold and Snow

Crazy Horse — Tue, 09 Aug 2005 15:00:00 -0400

Let x be "it is cold" and let y be "it is snowing". Describe each of the following:

(1) ~x

(2) x ^ y

(3) ~x ^ ~y

(4) ~(~y)

Derivatives

Crazy Horse — Fri, 05 Aug 2005 17:00:00 -0400

Find the derivative for the following:

f(x) = 3x6 + 5x - 4

Propositions

Crazy Horse — Tue, 26 Jul 2005 14:14:00 -0400

Verify that the proposition (p ^ q) ^ ~ (p v q) is a contradiction.

Related Rates

Crazy Horse — Sat, 23 Jul 2005 14:14:00 -0400

As a last ditch attempt to destroy a meteor propelling towards Earth, NASA scientists decide to launch a nuclear warhead. As the two converge, the missile and the meteor are at right angles to each other. The nuke is 700 miles away from the point of impact and traveling at 900 MPH; the meteor is 500 miles from impact and traveling at 1100 MPH.

(1) At what rate is the distance between the two decreasing?

(2) How much time until they converge?

(3) Since the beginning of the war in Iraq, how many people have died in the US due to inflated defense budgets in lieu of increased health department budgets?

Snowballs

Crazy Horse — Wed, 13 Jul 2005 21:36:00 -0400

A snowball rolls down a hill gathering snow as it rolls and keeping perfectly spherical shape as it goes.

Least Squares

Crazy Horse — Fri, 08 Jul 2005 21:25:00 -0400

Use the method of least squares to find a line that best fits the points (-1,-1) (0,0) and (2,1). Use this to estimate the value of y when x = 1.

Cool calculus resources:

Calculus on the Web

BOTW Math

Calculus Solutions

Derivative

Crazy Horse — Wed, 06 Jul 2005 13:23:00 -0400

Compute the derivative of the following equation:

f(x) = x³(2x+4)²

Implicit Differentiation

Crazy Horse — Sun, 03 Jul 2005 11:19:00 -0400

Let x^1/2+y^1/2=a^1/2. Find y' using implicit differentiation.

Velocity

Crazy Horse — Thu, 30 Jun 2005 11:36:00 -0400

An object moves in a wind tunnel along a straight line path so that the distance in feet it has traveled after t seconds is given by s=20t-t^3/2

(1) What is the average velocity of the object during the time interval [2.5,5.4]?

(2) What is the instantaneous velocity at time t = 3 seconds?

Derivatives

Crazy Horse — Tue, 28 Jun 2005 16:58:00 -0400

Determine a so that f(x) is continuous at every point:

Power Substitution

Crazy Horse — Mon, 27 Jun 2005 17:37:00 -0400

Integrate the following

*HINT - Remove the ``outside" square root first and use the power substitution

Logarithmic Differentiation

Crazy Horse — Sun, 26 Jun 2005 09:27:00 -0400

Consider the function

Determine the slope of the line perpendicular to the graph of f at x=1 .

Squeeze Principle

Crazy Horse — Fri, 17 Jun 2005 14:27:00 -0400

Given that:

Show that f is continuous at x=0