Respuesta :

LammettHash

If [tex]f(x) = x^2 + 3[/tex], then

[tex]x = 1.1 \implies y = f(1.1) = 1.1^2 + 3 = 4.21 \\\\ \implies m_{\rm sec} = \dfrac{4.21-1}{4-1} = \dfrac{3.21}3 = \boxed{1.07}[/tex]

[tex]x=1.01 \implies y = f(1.01) = 4.0201 \\\\ \implies m_{\rm sec} = \dfrac{3.0201}3 = \boxed{1.0067}[/tex]

[tex]x=1.001 \implies y=f(1.001) = 4.002001 \\\\ \implies m_{\rm sec} = \dfrac{3.002001}3 \approx \boxed{1.0007}[/tex]

[tex]x=1.0001 \implies y = f(1.0001) = 4.00020001 \\\\ \implies m_{\rm sec} = \dfrac{3.00020001}3 \approx \boxed{1.0001}[/tex]

xero099

The slopes of the secant lines are listed below:

  1. Δx = 0.1 → m = 2.1
  2. Δx = 0.01 → m = 2.01
  3. Δx = 0.001 → m = 2
  4. Δx = 0.0001 → m = 2

How to calculate the slope of a secant line related to a function

Herein we know a quadratic equation and the x-coordinates associated to line secant to the curve, of which we are supposed to determine the measure of the slope of that line by using the following expression:

m = [f(x + Δx) - f(x)] / [Δx]          (1)

If we know that f(x) = x² + 3 and x = 1, then the slopes of the secant lines are, respectively:

Δx = 0.1

f(1) = 1² + 3

f(1) = 4

f(1.1) = 4.21

m = (4.21 - 4) / 0.1

m = 2.1

Δx = 0.01

f(1.01) = 1.01² + 3

f(1.01) = 4.0201

m = (4.0201 - 4) / 0.01

m = 2.01

Δx = 0.001

f(1.001) = 1.001² + 3

f(1.001) = 4.002

m = (4.002 - 4) / 0.001

m = 2

Δx = 1.0001

f(1.0001) = 1.0001² + 3

f(1.0001) = 4.0002

m = (4.0002 - 4) / 0.0001

m = 2

To learn more on secant lines: https://brainly.com/question/14438198

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