Alright, another week of Calculus down. I studied, failed, and learned this week. I do understand most of the related rates problems and more of limits, but I am still having trouble with things we learned last week.
I really understand problems like these so, let me do one:
The radius, r, of a circle is increasing at a rate of 2 centimeters per minute. Find the rate of change of area, A, when the radius is 10.
1. It helps me to copy down what is given and what I'm trying to exactly find:
A=(pi)r^2
dr/dt= 2
r= 10
dA/dt= ?
2. You then take the derivative of the formula, and plug in your given:
dA/dt= 2r(dr/dt)(pi)
dA/dt= (2)(10)(2)pi
dA/dt= 40pi
Also, we went over limits this week which I'm understanding better.
Rules for Limits:
1. if the degree of top equals thedegree of bottom, the answer is the top coefficient over bottom coefficient
2. if top degree is bigger than bottom degree, the answer is positive or negative infinity
2. if top degree is less than bottom degree, the answer is 0
B-rob also stressed to us that problems when you have to plug in and the denominatior equals zero then you have to either factor and cancel OR plug into your calculator.
For what I don't understand:
angle of elevation and linearization
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In linearization the key word is approximate.
ReplyDeleteThe type we saw the most so far is use differentials to approximate something.
For these:
1. identify an equation
2. f(x)+f'(x)dx is the equation you use
3. determine dx
4. determine x
5. plug dx and x into the equation
Example:
use differentials to approximate the square root of 36.8
1. the equation: the square root of x
2. to find f'(x), you have to take the derivative of the square root of x, which is 1/2 square root of x
so your equation is now the square root of x + 1/2 square root of x dx
3. dx= .8
4. x= 36
5. plug in: the square root of 36 + 1/ 2 the square root of 36 (.8)
when figured out the answer is: 6.0667
To the find error in this, you subtract the total you have from the actually total of the square root of 36.8
In this problem it would be .0003
angle of elevation is my new given expertice so your in luck...lol. Alright so remember these steps and it will help.
ReplyDelete1)read your problem and determine what they are asking for and right down your given.
2)draw your triangle and right in your given and what your looking for on your triangle.
3)determine what equation they want you to lose. Area or pathagoreons thereom mostly.
4) take your derivative of the equation being sure to take the derivative with respect to time.
5)you then plug in your given and solve for the unknown.
These steps are the steps that i follow and that help me the best
I think these two explainations helped me figure this out! Thanks guyss :D
ReplyDeleteRyan excellent job explaining angle of elevation.
ReplyDelete