Question

use a numerical method to estimate the value of the limit (if it exists.) Lim e^5t -1 /t as x tends to 0 from both sides​

Answer 1

Hello from MrBillDoesMath!

Answer:

5

Discussion:

Consider the expansion of e^x:

e^x = 1 + x + x^2/2 + x^3/6 +...... => replace x by 5t

e^(5t) = 1 + (5t) + (5t)^2/2 + .... => subtract 1 from both sides

e^(5t) - 1 = (5t) + (5t)^2/2+.... => divide both sides by t

(e^(5t) -1)/ t = 5 + (25/2) t +....

so as t ends to 0 the quotient tends to

5 + (25/2)0 + (other terms) *0 -> 5

Thank you,

MrB