Mastering Limits: Solving Infinity and Radical Problems with Sin and Cos

[EasyStyle4747]

limits help!

ok I am going to try my best to express these problems because I don't really know how to get some of these symbols. If someone knows how to represent these:

infinity
radical

please tell me.

On to the problems (we need to find the limit):

1)
lim x / radical(x^2-x)
x-> -infinity

I basically tried multiplying the denom. to the denom and num to get rid of the radical. But then what?

2) I don't really understand these sin cos things (again find limit).
a)
lim (x-cosx)/x
x-> infinity

b)
lim 1/(2x+sinx)
x-> infinity

c)
lim cos(1/x)
x-> infinity

d)
lim (sin2x)/x
x-> infinity

I don't need all of these to be done, just choose which one u think is the easiest to explain and explain the best u can to me. thank you.

 

[faust9]

1) How did you do this one?

2) a)You can split the numerator up can't you? \frac{2+3}{8}=\frac{2}{8}+\frac{3}{8}=\frac{5}{8} I know it's a rudamentry example but it shows what I mean. Also aren't sin and cos functions limited to 1 or -1? Do you know hwo to deal with functions that oscillate? Do you know L'Hopitals?

b) Again, sin and cos functions oscillate between -1 to 1. Think about it now, would ±1 have a big effect on (2*infinity)?

c) what is 1/infinity What is the cos of that result?

d) see above.

 

[EasyStyle4747]

i dun quite understand what you mean when you say would +-1 have a big effect on (2*infiinity).

 

[ShawnD]

Damn. I thought I had the answer to 1, but a second look spotted errors

 

[Hurkyl]

You do (1) in exactly the same manner as if both the numerator and denominator were polynomials... the degree of the numerator is 1, and the degree of the denominator is 1 (1/2 * 2), so...