Lets just jump right in to an example problem since I'm great at these:
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 4.
A= pi(r)2 dr/dt=2 dA/dt=?
2(pi)r(dy/dt)
2(pi)(4)2
2(pi)8
= 16pi
These are real simple. First, I identify what the problem is trying to find. Then I copy what is given. These problems usually involve the area of a circle or volume of a cone or sphere. So, we should probably start memorizing those. After, take the derivative of the equation and just plug in.
Another example problem, just because I love doing these:
A point is moving along the graph of the function y=sin3x such that dx/dt=2 centimeters per second. Find dy/dt when x=pi/7.
y=sin3x dx/dt=2 dy/dt=?
dy/dt= cos3x(3)dy/dx
cos3(pi/7)(3)2
dy/dt= cos 3pi/7(6)
dy/dt- 6cos(3pi/7)
Also, I understand how to find d^2y/dx^2, but for some reason I have trouble getting the right answer. I think I might just make stupid little mistakes.
Soooo for what I'm still having major trouble with:
Angle of Elevation
linearization: like use differentials to approximate the square root of 16.5
Help please :)
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LE2010 said...
ReplyDeleteLinearization:
the keyword is APPROXIMATE
Using differentials, we learned how to approximate.
For example:
APPROXIMATE the square root of 99.4
f[x]=the square root of [x]
f(x)+f'(x)[dx] : the square root of [x] + [1/2*the square root of [x]]*[dx]
dx = .4
x = 99
plug in:... the square root of 99 + [(1)/(2*the square root of 99)]*[.4]
giving you...9.96997
when we plug in the square root of 99.4 in our calculater we are only 0.00002 off so that's our error!
For angle of elevation, use
ReplyDeletetan(theta)=x/y
sin(theta)=y/hypot
cos(theta)=x/hypot
Then you take the derivative...and solve? I think..maybe...that's what I got out of it...you might want to double check before the tests
use sohcahtoa and take the derivative
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