anonymous
  • anonymous
Plz some one help!!! Part a: Constract an infinitely differentiable function which vanishes outside a given finite interval [a,b]. Hint: Consider this function \[g(x) = e ^{-1/x ^{2}} \] if x>0 and 0 for x<=0 Part b: Constract a infinitely differentiable function which is 0 forx<=a and 1 for x>=b (a
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Whimsical
  • Whimsical
i am not sure about what the question is trying to ask us to find, however my g'(x) is (2x^-3)(e^-x^-2)
anonymous
  • anonymous
by saying the differentiable function vanishes outside a finite interval [a,b], you mean it doesn't exist for all x>b and x
anonymous
  • anonymous
I'll try my best to help so for part a.) consider the square root function, \[\sqrt{4-(x-2)^2}\] Notice that if we graph this function, it vanishes outside the interval [0,4]... now since the function is defined and is continous on the interval [0,4] or for 0<=x<=4, then it is differentiable on any point on that interval, hence it must be infinitely differentiable function which vanishes outside the finite interval [0,4]

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anonymous
  • anonymous
thx a lot. Looks good.
anonymous
  • anonymous
can I ask what you mean by an infinitely differentiable function?
anonymous
  • anonymous
function that has derivatives of all orders
anonymous
  • anonymous
ah.. So I could continue to differentiate it forever without ending up with zero right?
anonymous
  • anonymous
right
anonymous
  • anonymous
ok so my previous answer was wrong :))
anonymous
  • anonymous
kindly disregard that :))
anonymous
  • anonymous
why?
anonymous
  • anonymous
your function derivative never 0
anonymous
  • anonymous
sorry carelessness :))
anonymous
  • anonymous
any posiblilities to make it exponential function?
anonymous
  • anonymous
yes, that's if the base is between 0 and 1

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