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-(1/t)2for t02.65. If f(t) =show that f(n) (0) = 0 for all nfor t= 0'

Question
-(1/t)2
for t0
2.65. If f(t) =
show that f(n) (0) = 0 for all n
for t= 0'
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-(1/t)2 for t0 2.65. If f(t) = show that f(n) (0) = 0 for all n for t= 0'

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Step 1

To show that the function f(x) , as defined , has all its derivatives 0 at x =0

Step 2

To start with, f(t) is well defined and continuous...

f()exp(
.t 0
= 0,t 0
Now. f() is well -defimed,and
1
)
(because, lim-
lim f
0
so, f(t) is continuous at t = (0
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f()exp( .t 0 = 0,t 0 Now. f() is well -defimed,and 1 ) (because, lim- lim f 0 so, f(t) is continuous at t = (0

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