Lets say they want to know the rate of change of the volume of a sphere:
the radius is 5, and the rate of change of the sphere is 10. Find Dv/Dt.
the formula for the volume of a sphere is:
V= 1/3(pi)(r^3)
so from here you can plug in the given:
V=1/3(pi)(5^3)(10)
now take the derivative of the function:
dV/dt=(pi)(5^2)(10)
now you can simplify and solve for dV/dt:
dV/dt= 250(pi)
Now lets look at an example of limits:
Find the limit as x goes to infinity
x^3-8
-------
2x^3-4
in this problem we can use our limit rules. Since the degree on the top is the same as the degree on the bottom, the answer will be the coefficients:
so the answer is x-> infinity is 1/2
Some of the things i still do not understand is angle of elevation, and optimization. When dealing with optimization, once i figure out what my formulas are, i can work the problem from there, but i still have trouble figuring out the formulas and drawing a picture to find the formulas. When dealing with angle of elevation, i do not even understand where to start. I do not know how it is different from related rates and i need somebody to explain exactly what i'm looking for and what i need to work the problem. If anyone can help me out i would really appreciate it. Thanks :)
Angle of Elevation is not different from Related Rates. It's the same thing. Only thing difference is the formula you using.
ReplyDeleteThe formula you use is either
tan(theta) = x/y where either x is constant or y is constant
or sin(theta) y/hyp where hyp is constant
or cos(theta) x/hyp where hyp is constant again.
After you identify which equation will work best for you, its the same steps as related rates.
Ok, for picking optimization equations, you always look for what the number given is equal to and what it asks you to optimize. If a question states:
ReplyDeleteThe perimiter of a rectangle is equal to 24 with a maximum area.
The way I look at it, the secondary equation will always be the one set equal to a number, in this case, and in most cases with area, it is the perimiter. You also know your primary equation is area because it says to maximize it. When looking at these problems always look for the words maximize or minimize. They will always be connected to your primary equation.
angle of elevation: you mainly use the things like SOHCAHTOA u would use tan(theta)=opossite/adjacent. you just use the sides to find the angle
ReplyDelete