How to solve

[Valentas]

OUR TEACHER, AS ALWAYS GAVE US HOMEWORK, WHICH SHE DID NOT EXPLAIN

\(\displaystyle e^{x+2}-1 = 0 \)

Probably the answer is x = -2 but I don't know how to show it mathematically...

NEXT

I've been searching for derivative and found this:

\(\displaystyle \frac{e^3 - e^x}{e^x} < 0 \)

I know that it is not allowed to multiply both sides from denominator in inequalities so I stuck there.. Maybe it's simple but I'd like that you show me how to solve this

 

[pka]

\(\displaystyle e^{x+2}-1 = 0 \)
Probably the answer is x = -2 but I don't know how to show it mathematically...

NEXT
\(\displaystyle \dfrac{e^3 - e^x}{e^x} < 0 \)

For the first, \(\displaystyle e^0=1\) that is all there is to it.
Just say \(\displaystyle x+2=0\) so \(\displaystyle x=-2\)

In the second, the denominator is always positive so you must have \(\displaystyle e^3-e^x<0\) so \(\displaystyle e^3<e^x\) or \(\displaystyle 3<x\).

 

[mmm4444bot]

OUR TEACHER, AS ALWAYS GAVE US HOMEWORK, WHICH SHE DID NOT EXPLAIN

Since you shouted this information, it must be important to you.

There is a simple explanation.

Teachers do not explain how to do each exercise assigned because students are expected to do some thinking on their own.