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  1. mathematics
  2. basic math
  3. let f(x) = (x − 1)2, g(x) = e

Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at  a = 0. Lf (x) =    Lg(x) =    Lh(x) =  (b) Graph f, g, and h and their linear approximations....

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Basic Math

Let f(x) =(x − 1)2, g(x) = e−2x,and h(x) = 1 + ln(1 − 2x).

(a) Find the linearizationsof f, g,and h at 

a = 0.

Lf (x) = 

 

Lg(x) = 

 

Lh(x) = 

(b) Graph f, g,and h and their linear approximations. For whichfunction is the linear approximation best? For which is it worst?Explain.

The linear approximation appears to be the best forthe function  ? f g h since it iscloser to  ? f g h for a largerdomain than it is to  - Select - f and g g andh f and h . The approximation looks worstfor  ? f g h since  ? f g h movesaway from L faster than  - Select- f and g g and h f and h do.

Use differentials to estimate the amount of paintneeded to apply a coat of paint 0.04 cm thick to ahemispherical dome with diameter 44 m. (Round your answerto two decimal places.)
  m3  

Answer & Explanation Solved by verified expert
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let y fx is the function to find local linear approximationat x x0 we need to find equation of tangent to    See Answer
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