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it's not equal to zero since infinity isn't technically a number (so division isn't really defined)
but you can think of it in terms of limits: as x gets bigger and bigger in a/x, then a/x becomes smaller and smaller and it will approach 0
It's just like an approximation then. How about infinity over a number, its the same process
infinity over a number is also not really defined, but you can think of it as
x/a approaches some very large number (infinity) as x ---> infinity
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Okay makes sense Thanks. Can you help me on Order Of Magnitude please?
what do you mean
Determine whether the function grows faster than e^x, at the same rate as e^x, or slower than e^x as x --> infinity.
I don't understand how to solve the problem analytically. Do I move x to the denominator?
x*e^x grows faster because e^x grows fast on its own, but if you multiply it by some positive number (which is growing somewhat fast, but not as fast as e^x), then x*e^x will grow that much faster than e^x alone
Okay so how about if the directions say Show that x^2 grows at the same rate as the function F(X)= x^2 + sinx. The directions are asking me to prove it, so do I have to do L'Hopitals Rule?
not sure how to rigorously prove it, but you can point out that because sin(x) is periodic, it doesn't really add to the growth of x^2