To find: limx→∞ e-2x cosx
Answer: limx→∞ e-2x cosx=0
Since cosx is a bounded function (bounded below by -1 and bounded above by 1), no matter how large is the value of x, cosx is always finite. Whereas e-x 0 as x ∞.
So, the required limit is 0 * (a finite number, which is in (-1,1))=0
i.e., limx→∞ e-2x cosx=0.
Note: The symbol * stands for multiplication.
limx→∞ e-2x cosx=0