How do you use the squeeze law of limits to find a limit involving a third root?

[Monsu]

i am quite confused with that law, would someone pls just explain it ina few words?
well, the actual question goes like this:
Use the squeez law of limits to find lim x->0 x^2cos(1/thirdrootx).

(third root of 8 = 2 , 2x2x2 = 8, in case u do not understand what i mean by third root, i can't type the sign)

 

[Pyrrhus]

well if you graph cos you will notice it oscillates (sp?) between -1 and 1, so if you multiply cos(angle) with x^2 it will have a "amplitud", new max values between x^2 and -x^2.

so if you know the limit of x^2 and -x^2 you will know where does cos(angle) goes. I forgot and if the limits of both are the same!, very important.

 

[Monsu]

so whatever happens to the 1/thirdrootX ??

 

[Pyrrhus]

so whatever happens to the 1/thirdrootX ??

Try many values in the calculator of any form with cosine and see what you observe.

 

[Monsu]

Got it! thanks.