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13 Nov 2019
Part 2: Derivatives of Exponentials. Recall that the derivative of a function f(z) at a point a is equal to the limit So if f(x)-b then the derivative of f(z) at z -0 is equal to the limit lim If we evaluate this limit for b = 2 we get 0.69315 and if b = 3 then the limit is 1.0986. So if there is a b so that the limit is equal to 1 it must be between 2 and 3. We will try to find this particular value of b by using the bisection method. Since 2 gave a limit that was too small and 3 gave a limit that was too big we will next try b=2.5 ë¶ This gives a limit of 0.9163 which is less than 1. So let's try b-275-22t3 which gives a limit of 1.0116 which is greater than 1. Now since the limit was greater than 1 for b 2.75 and less than 1 for b 2.5 the next number to try is b = 2.625 = 275+25 2 What limit does this value of b give us? Continue finding new values of b using this bisection method until the limit is within 0.001 of 1. What value of b did you end with? How does this value compare to the constant e?
Part 2: Derivatives of Exponentials. Recall that the derivative of a function f(z) at a point a is equal to the limit So if f(x)-b then the derivative of f(z) at z -0 is equal to the limit lim If we evaluate this limit for b = 2 we get 0.69315 and if b = 3 then the limit is 1.0986. So if there is a b so that the limit is equal to 1 it must be between 2 and 3. We will try to find this particular value of b by using the bisection method. Since 2 gave a limit that was too small and 3 gave a limit that was too big we will next try b=2.5 ë¶ This gives a limit of 0.9163 which is less than 1. So let's try b-275-22t3 which gives a limit of 1.0116 which is greater than 1. Now since the limit was greater than 1 for b 2.75 and less than 1 for b 2.5 the next number to try is b = 2.625 = 275+25 2 What limit does this value of b give us? Continue finding new values of b using this bisection method until the limit is within 0.001 of 1. What value of b did you end with? How does this value compare to the constant e?
Reid WolffLv2
26 Oct 2019