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solve sin 3t 2 solutionthis example is designed to remind you of certain properties about sine and cosine recall that -1 le sin theta le 1 and
solve sin alpha 7 0 solutionby using a unit circle it isnt too difficult to see that the solutions to this equation arealpha 7 0 2
solve cos 4 theta -1 solutionthere actually isnt too much to do along with this problem however it is different from all the others done to
decimal representations of some basic angles as a last quick topic lets note that it will on occasion be useful to remember the decimal
solving trig equations with calculators part i the single problem along with the equations we solved out in there is that they pretty much all had
our objective is solve the following fourth-order bvp axu f x u0 u10 u0 u10 a give the variational formulation
euler equations - series solutions to differential equations in this section we require to look for solutions toax2 yprimeprime bxyprime cy
once we get out of the review we are not going to be doing a lot with taylor series but they are a fine method to get us back into the swing of
given f x 3x - 2 determine f -1 x solutionnow already we know what the inverse to this function is as already weve done some
finding the inverse of a function the procedure for finding the inverse of a function is a rather simple one although there are a couple of steps
definition of inverse functions given two one-to-one functions f x and g x if f o g x x and g o f x xthen we say that f x
one-to-one function a function is called one-to-one if not any two values of x produce the same y mathematically specking this is the same as
inverse functions in the last instance from the previous section we looked at the two functions f x 3x - 2 and g x x 3 23 and saw that f o
function composition the next topic that we have to discuss here is that of function composition the composition of fx amp gx is f o g x f g x
determine the domain of each of the following functions f
domain and range of a functio one of the more significant ideas regarding functions is that of the domain and range of a function in simplest
write down the system of differential equations for the population of both predators and prey by using the assumptions abovesolutionwe will start off
the next kind of problem seems as the population problem back in the first order modeling section we looked at several population problems in such
given f x - x2 6 x -11 determine each of the followinga f 2b f -10c f t solutiona f 2 - 22 62
two 1000 liter tanks are containing salt water tank 1 has 800 liters of water initially having 20 grams of salt dissolved in this and tank 2 has 1000
function notation next we have to take a rapid look at function notation function notation is nothing more than way of writing the y in a function
definition an equation is considered as function if for any x in the domain of the equation the domain is the entire xs which can be plugged into the
under this section were going to go back and revisit the concept of modeling only now were going to look at this in light of the fact as we now
in this case we will require deriving a new formula for variation of parameters for systems the derivation now will be much simpler than the when
undetermined coefficientsthe way of undetermined coefficients for systems is pretty much the same to the second order differential equation case the