Question

Question #6f5b6

Answer 1

See the explanation section.

Explanation:

Here are `y=e^x` and `y=1+x` on the same coordinate system near `0`. (You can scroll in or out and drag the graph around with a mouse.)

graph{(y-e^x)(y-(1+x))=0 [-5.723, 6.763, -2.37, 3.873]}

We can see that the curves are close to each other.

To answer the second question we can graph the difference,

`y=e^x-(1+x)` and try to determine when `y` is between `-0.1` and `0.1`

graph{y=e^x-(1+x) [-1.085, 1.049, -0.406, 0.66]}

I prefer to graph `y = [e^x-(1+x)]-0.1` . The difference between `e^x` and `1+x` is less than `0.1` when this `y` is negative. So we just find the `x` intercepts: approximately `-0.483` and `0.416`

graph{y = e^x-(1+x)-0.1 [-1.923, 1.922, -0.959, 0.963]}