Post #29

Another week down...

Let’s see what I remember shall we.. if you take the derivative of f^2(x) you treat it as if it was like sine. You do 2f(x) times f’(x) times 1. So it’s almost as if you have (f(x))^2 and you use the chain rule. Bring the 2 to the front, subtract 1, times by the derivative of the inside. And since the derivative of f(x) is f’(x) times the derivative of x, which is 1. These rules seem to help me A LOT!

Lets say you have:
x^2-2 DIVIDED BY 4-x^2 AS THE LIMIT APPROACHES 2
soo..
for this you end up getting two divided by zero. For finite limits though, if you get a number over zero, it’s always infinity. Therefore the answer is INFINITY!

Remember:
If the top exponent is greater than the bottom it’s the limit as it approaches infinity, and if the top exponent is less than the bottom it’s the limit as it approaches zero!
DON’T GET THEM CONFUSED LIKE I DID!
Here’s a trick:
Remember if you’re divided a number by another number and you have a bigger number on top it’s usually not zero. Also, if you’re dividing a number by another number and you have a smaller number on top it’s usually not a big number. Therefore, when the bigger number is on top since it’s a bigger number than zero it’s INFINITY and when the bigger number is on the bottom that means that it’s being lessened so it’s ZERO!

volume by disks
so you know that the formula is pi times the integral of the [function given] squared times dx. well then you gotta know what to do right so just solve it by taking the integral of it and then pluging in the numbers they give you. just like before you'll have two numbers so whatever the answer is for the top one will be first and then you subtract the answer you get for the bottom one...oh, REMEMBER TO GRAPH..
just look at what they give you...they're should be numbers that they want them inbetween
IF NOT..WHAT DO YOU DO???

volume by washers
so you know that the formla is pie times the integral of the [top function] squared minus the [bottom function] squared times dx. so to do this, if you don't have the inbetween number you have to set the functions equal, but if you do, then it's worked the same way as above. square the formula's that were given and simplify. then take the integral of it and plug in the numbers they give you or you found by setting the formulas equal to each other and then solve like any other one by subracting them. REMEMBER TO GRAPH!

just a reminder if it's for the x-axis then you solve for y and if it's on the y-axis then you solve for x..and if you plug the y-axis one's in your calculator to graph then you'll have to turn your calculator sideways with the screen on the right to see how it would really look.

area...it's worked the same just they'll give you two equations and if you don't have numbers for the inbetween then you'll set them equal to get them, but if you do then don't worry and keep going. for area there is no pi and no squaring. so you put the integral of the first equation minus the second equation and simplify and solve. then take the integral of it and plug in the numbers inbetween!

examples:

AREA:
y=-4x^2+41x+94 AND y=x-2 inbetween 7 and 1
so graph and then put the top equation over the bottom equation
the integral of (-4x^2+41x+94)-(x-2)dx
simplify: the integral of (-4x^2+40x+96) dx
((-4/3)(x)^3+20(x)^2+96(x)) of 1 and 7
f(7)=(3584/3) f(1)=(344/3)
ANSWER: 1080

VOLUME:
y=the sqr. root of (-2(x)^2-10(x)+48) inbetween 1 and -2
so graph and then put take the equation they give you into the integral and square it
PI times the integral of (-2(x)^2-10(x)+48) dx
PI [(-2/3)(x)^3-5(x)2+48(x)] of 1 and -2
f(1)=(127/3) f(-2)=(-332/3)
ANSWER: (153 PI)

hope this helps...

~ElliE~