Write the equation of the line that represents the linear approximation to the following function at the given point a. b. graph the function and the linear approximation at a. c. use the linear approximation to estimate the given function value. d. compute the percent error in your approximation, 100 |approx - exact| / |exact|, where theexact value is given by a calculator. f(x) = 7 - x^2 at a = 2; f(1.9) l(x) =

  a, b.  see below

  c.  L(1.9) = 3.4

  d.  f(1.9) = 3.39; error ≈ 0.29%

Step-by-step explanation:

a. A graphing calculator is useful for graphing these functions.

b. The linear approximation at x=2 is ...

  L(x) = f'(2)(x -2) +f(2)

The derivative is ...

  f'(x) = -2x

so the linear equation is ...

  L(x) = (-2(2))(x -2) +(7 -2^2) = -4x +8 +(7 -4)

  L(x) = -4x +11

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c. L(1.9) = -4(1.9) +11 = 3.4

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d. f(1.9) = 7 -(1.9^2) = 7 -3.61

  f(1.9) = 3.39

  percent error = ((3.4 -3.39)/3.39)×100% ≈ 0.29%

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m