contestada

a. Use your calculator to approximate ∫^ b_0 e^-0.00001x dx for b=10, 50, 100 and 1000.
b. Based on your answers to part a, does ∫^[infinity]_0 e^-0.00001 dx appear to be convergent or divergent?
c. To what value does the integral actually converge?

Respuesta :

Answer:

Step-by-step explanation:

We are to integrate the function

[tex]e^-0.00001x[/tex] from 0 to b for different ascending values of x.

[tex]\int e^-0.00001x = -10^5 e^-0.00001x[/tex]

Now we substitute the limits

When b =10

I = integral value = [tex]-10^5 e^-0.00001*10[/tex]

b =50, I = [tex]-10^5(e^-0.00001*50-1)[/tex]

b =100, I = [tex]-10^5( e^-0.00001*100-1)[/tex]

b =1000 I=  [tex]-10^5 (e^-0.00001*1000-1)[/tex]

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  [tex]-10^5 (0-1)[/tex]=10^5