A. use your calculator to approximate ∫^ b_0 e^-0.1x dx for b=10, 50, 100 and 1000.
b. based on your answers to part a, does ∫^[infinity]_0 e^-0.1 dx appear to be convergent or divergent?
c. to what value does the integral actually converge?

Step-by-step explanation:

We are to integrate the function

from 0 to b for different ascending values of x.

Now we substitute the limits

When b =10

I = integral value =

b =50, I =

b =100, I =

b =1000 I=  

b) As b increases exponent increases in negative, or denominator increases hence when b becomes large this will be a decreasing sequence hence converges

c) Converges to  =10^5