Post -.-

Well, since my mother decided to destroy not only my phone (by dropping it in water, purposely) but also my internet, it was unable to submit my blog by 12 on Sunday night, or rather Monday morning, So. here it is..from my laptop at school. Monday morning, Yes, I'm a tad bit angry...

Okay, since I've repeated steps possibly a thousand times and have seen them on blogs for I don't know how long, I'm just going to do a couple of example problems that actually apply the aforementioned (I LOVE that word!) steps.

Okay, so examples...:

EXAMPLE 1:Given the equation y = (x-3)/(2-5x). Find dy/dx.

Quotient Rule (you could technically do product, but I prefer things set in stone (plug into a formula nd all))

dy/dx = ((2-5x)(1) -(-5)(x-3))/(2-5x)^2
= (2-5x + 5x -15)/(2-5x)^2
= - 13/(2-5x)^2

What I did: I took the derivative of the function using the quotient rule**be sure not to mix up NEGATIVES!!


EXAMPLE 2: What is the maximum value for the following: f(x) = xe^-x

Take derivative using product rule (multiplying two things).

x(-e^-x) + e^-x(1)remember that the der. e is e^w/e times the der. of the exponent

Simplify:
-xe^-x + e^-x

You can factor out an e^-x

(-x+1)e^-x

To find the critical values (possible maxima) set (-x+1) equal to zero and solve for x.

This yields x = 1. Now plug in that one to e^-x.

This then gives you 1/e====>your maximum value.


EXAMPLE 3: The table shows the speed of an object in feet per second, during a 3 second period.

time(sec)-----0--1--2--3
speed(ft/sec)-30-22-12-0

Estimate the distance traveled using the trapezoid method.

All you have to do for this particular problem is find delta x then plug into the formula: delta x /2 [f(first one) +2f(next)...f(last one)]

b-a/n = delta x

3-0/3 = 1

1/2[30 + 2(22) + 2(12) + 0]

1/2[20 + 44 + 24]
=49

EXAMPLE 4: Which best describes the behavior of the function y = arctan(1/lnx) at x = t?

A. It has a jump discontinuity
B. It has an infinite discontinuity.
C. It has a removable discontinuity
D. It is both continuous and differentiable
E. It is continuous but not differentiable.

Now since I found this question on a calculator portion, I would first graph it...which I believe to be a very obvious course of action, but whatever. So, I know the answer, but maybe just maybe, you should try it yourself??

Okay, I've got to go. Have a nice week!