Question

ANSWER THIS MATH QUESTION

Answer 1

Answer:

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

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.