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)

Find the derivative for the following:

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

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

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?

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

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

Compute the derivative of the following equation:

f(x) = x³(2x+4)²

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

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?

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

Integrate the following



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

Consider the function



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

Given that:



Show that f is continuous at x=0