#### To determine

**To find**: limx→∞ e-2x cosx

#### Answer

**Answer: limx→∞ e-2x cosx=0**

#### Explanation

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.

**Conclusion:**

**limx→∞ e-2x cosx=0**