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What's the Difference Between a Computer Keyboard and a Typewriter ?

The standard computer keyboard is based on those used on typewriters. Both have what is called a QWERTY keyboard arrangement of the keys. A standard typewriter does not have as many keys as a standard computer keyboard. Missing are the 10 keys (number pad to the right on most standard PC keyboards). The F1 - F12 or Function keys, ESC, Print Screen, Scroll Lock, Pause, Insert, Home, Page Up & Down, Delete, End, cursor or arrow keys, the CTRL, ALT and Windows key (on Windows based PCs) and most notability the Enter key. Several keys on a computer keyboard also have a Shift, CTRL and Alt function not found on the standard typewriter. Along with those there are also some combinations of keys to provide other functions depending on the program its being used with a PC. Many typewriters also have slightly different arrangements of some of their keys. I've see some with no number one, instead requiring the use of a lower case L. I've also seen several which do not strictly follow the QWERTY layout of keys. Take a look at images of a Typewriter keyboard in Google and compare to your PCs keyboard. There can be some signification differences.

What's the Difference Between a Computer Keyboard and a Typewriter ? 1

1. my gear shift does not work on my ford focus automatic it doesn't want to come out of park?

Are your brake lights inoperative also? your car has a gear shift lock-out that releases when you step on the brake pedal, the power to this lock-out solenoid comes from your brake-lite switch, so here is the drill #1 make sure your cars front tires are not resting into a curb or parked on a sharp downgrade., this may put stress on the shifter #2check the fuses for the brake lites, relace as applicable #3check the brakelite switch for function (highly probable) #4check the wiring and gear shift lock-out solenoid. Thats pretty much it, If fuses continue to break its a hard fault that will need chasing, bad wiring,solenoid, switches. . etchope this helps, good luck.

2. Is this function one to one?

Yes, f(x) is one-to-one. Here is how to prove it. The domain of f(x) is (0, ). Let a and b be two values on that domain. Let f(a) = f(b). 1/(a) 1 = 1/(b) 1 1/(a) = 1/(b) (a) = (b) a = b So f(a) = f(b) only if a = b. By definition, f(x) is one-to-one (injective). And since the definition of f(x) has no conflicting range declaration, it is also onto (surjective). Together that means that f(x) does have an inverse. You did not ask for the inverse, but let me mention a pitfall to avoid. The range of f(x) = (1, ). That must also be the domain of f(x). f[f(x)] = x, for 1

What's the Difference Between a Computer Keyboard and a Typewriter ? 2

3. Evaluating an integral of a very large function multiplied by a very small function

If you rewrite the integral to be$$ int_0^t e^-a(t-t')P(t') dt'$$Then you should see that the integrand is dominated by the region where $t-t'approx 0$. Therefore, you write$$ int_0^t e^a(t'-t)[P(t) P'(t)(t'-t)...]$$ The zeroth order term is then $$ P(t)int_0^te^a(t'-t) = P(t)left(frac1-e^-ata

ight)approx fracP(t)a$$ You can find higher order terms using repeated integration by parts, but each term will be surpressed by another power of $a$ so if it is indeed extremely large, you wo not need many more. Quantities like $P'(t)$ can be evaluated by any number of numerical differentiation schemes if you cannot treat them analytically.

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