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Sliva [168]
3 years ago
10

Evaluate the function f (x) = -4x + 9 at f (3).

Mathematics
2 answers:
sweet [91]3 years ago
4 0
Substituting 3 for x:
-4(3)+9
-12+9
-3
Umnica [9.8K]3 years ago
3 0
<span>Plug in f(x) = 3 to solve 

</span>f (x) = -4x + 9

3 = -4x + 9 

3-9=-4x 

-6=-4x 

-6/-4=x 

6/4=x 

3/2=x 

x=3/2
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The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625

<h3>What is Riemann sum?</h3>

Formula for midpoints is given as;

M = ∑0^n-1f((xk + xk + 1)/2) × Δx;

From the information given, we have the following parameters

  • x0 = 0
  • n = 6
  • xn = 3

Let' s find the parameters

Δx = (3 - 0)/6 = 0.5

xk = x0 + kΔx = 0.5k

xk+1 = x0 + (k +1)Δx

Substitute the values

= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2

We then have;

= (0.5k + 0.5k + 05.)/2

= 0.5k + 0.25.

Now f(x) = 2x^2 - 7

Let's find  f((xk + xk+1)/2)

Substitute the value of (xk + xk+1)/2)

= f(0.5k+ 0.25)

= 2(0.5k + 0.25)2 - 7

Put values into formula for midpoint

M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.

To evaluate this sum, use command SUM(SEQ) from List menu.

M = - 12.0625

A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.

Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625

Learn more about Riemann sum here:

brainly.com/question/84388

#SPJ1

                                 

8 0
1 year ago
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