week 11 in calculus. we learned linearization.
linearization = approixmate. anytime you see the word "approximate" in a problem. it means to use linearization.
the formula for linearization: f(x) = f(c) + f(c)(x-c)
also, a differential is when something is solved for dy or dx.
alrighttttt, so. related rates are super easy now. ill explain those :)
you're given a problem usually something like, you have a spherical balloon going up, rate of change is ___ and dy/dx = ____ so find dx/dt. something like that.
^^^that type of problem requires you to draw out the picture yourself.
but you can also be given a picture with the problem, which can be very helpful.
steps, once again, are:
1. first identify all variables in equation
2. figure out what you want to find(what you are solving the equation for)
3. dont forget to sketch and label! *extra points
4. write an equation involving all your variables(plug in)
5. take derivative
6. solve
simple, right? kind of like optimization. but easier!
another recent thing we learned that is very simple. or i caught onto easily at least is implicit derivatives. you know it's an implicit derivative if you are given an x and y value in your equation. you simply take the derivative, noting all derivatives of y-values with dy/dx or y'. then solve for dy/dx or y'. it's quite easy.
what i don't understand: linearization and how to find angles of elevation.
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Linearization:
ReplyDeleteFirst off, the key word for linearization is approximate.
Example: Use differientials to approximate the square root of 25.7
Steps:
1. identify equation, in this case its the square root of x
2. f(x)+f'(x)dx, so the square root of x plus 1/2(the square root of x) times dx.
3. determine dx and x.
dx= .7; x= 25
4. plug into equation
the square root of 25 + (1/2(the square root of 25)) (.7)
which should equal: 5.07
For angle of elevation use these formulas
ReplyDeletetan(theta)=x/y
sin(theta)=y/hypot
cos(theta)=x/hypot