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yKpoI14uk [10]
2 years ago
14

ANSWER THIS MATH QUESTION

Mathematics
1 answer:
shusha [124]2 years ago
5 0

Answer:

<h2>The slope of the line tangent to the function at x = 1 is 2.01 ≅2.</h2>

Step-by-step explanation:

Using the formula of derivative, it can be easily shown that, \frac{d f(x)}{dx} = 2 where f(x) = x^{2}.

Here we need to show that as per the instructions in the given table.

Δy = f(x + Δx) - f(x) = f(1 + 0.01) - f(1) = (1 + 0.01)^{2} - 1^{2} = 0.0201.

In the above equation, we have put x = 1 because we need to find the slope of the line tangent at x = 1.

Hence, dividing Δy by Δx, we get, \frac{0.0201}{0.01} = 2.01.

Let's examine this taking a smaller value.

If we take Δx = 0.001, then Δy = 1.001^{2} - 1^{2} =  0.002001.

Thus, \frac{0.002001}{0.001} = 2.001.

The more smaller value of Δx is taken, the slope of the tangent will be approach towards the value of 2.

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