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xeze [42]
3 years ago
12

The graph of f(x) = x + 1 is shown in the figure. Find the largest δ such that if 0 < |x – 2| < δ then |f(x) – 3| < 0.4

.

Mathematics
2 answers:
MArishka [77]3 years ago
8 0
SO what you need to do is:
<span>Start with |f(x) - 3| < 0.4
and plug in f(x) = x+1
to get |f(x) – 3| < 0.4
|x+1 – 3| < 0.4
|x - 2| < 0.4
   -0.4 < x - 2 < 0.4
  -0.4+2 < x < 0.4+2
  1.6 < x < 2.4
So delta would be 2.3
Hope this is what you were looking for
</span>
Harrizon [31]3 years ago
4 0

The largest δ such that if 0 < |x – 2| < δ is 0.4

<h3>Further explanation</h3>

Solving linear equation mean calculating the unknown variable from the equation.

Let the linear equation : y = mx + c

If we draw the above equation on Cartesian Coordinates , it will be a straight line with :

<em>m → gradient of the line</em>

<em>( 0 , c ) → y - intercept</em>

Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :

\large {m = \frac{y_2 - y_1}{x_2 - x_1}

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

y - y_1 = m ( x - x_1 )

Let us tackle the problem.

Given:

f(x) = x + 1

If |f(x) - 3| < 0.4 , then :

|f(x) - 3| < 0.4

|x + 1 - 3| < 0.4

|x -2| < 0.4

Since the absolute value of a function is always positive, then:

0 < |x -2| < 0.4

From the relationship above, then the largest δ such that :

0 < |x - 2| < \delta

<h2>→ δ = 0.4</h2>

<h3>Learn more</h3>
  • Infinite Number of Solutions : brainly.com/question/5450548
  • System of Equations : brainly.com/question/1995493
  • System of Linear equations : brainly.com/question/3291576

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point

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