Division requires a larger computational budget than multiplication (computers are just like us, we hate long division!), which can cause issues in responsiveness of user interfaces, framerates in videogames, and the time needed to run simulations for important engineering problems. (a) Find the linearization, L(x), of f(x) = for x near 1. (b) It can often save significant time to use the above linearization to approximate x с ≈ CL(x), x since multiplication is computationally cheaper than division. For numbers x ≈ 1 the loss in accuracy is negligible compared to the gain in efficiency.

You can see that the amount of medication enters the therapeutic window quickly, but goes below the minimum near t=2.5 and exceeds the maximum near t=3.5. During the first time period (0 ≤ t ≤ ½), the medication is being released into the system, while there is also decay. In the second time period (½ ≤ t ≤ 3), the medication is no longer being released in the system, and decay is taking place. In the third time period (3 ≤ t ≤ 3.5), a second dose of the time release medication is given, etc. If dy/dt=f(t,y), you can write f(t,y) as a piecewise defined function with four pieces for each of the four intervals in which something different is happening. Recall from your readings that piecewise defined functions can be written as a single function by incorporating step functions and window functions (Section 7.6). In this discussion, you’ll examine other potential release and administration times to see if they stay within the therapeutic window. Assume the following: The decay rate for…

In this problem, we will use linearization to approximate the solution of et-1 = _t_ +1 which occurs near t=1. 20

1. A cement grinding mill “A” with a capacity of 50 tons/hr utilizes forged steel grinding balls costing P12,000/ton, which have a wear rate of 100 grams/ton cement milled. Another cement mill “B” of the same capacity uses high chrome steel grinding balls costing P50,000/ton with wear rate of 20 grams/ton cement milled. Determine the more economical grinding mill, considering other factors to be the same.