The notion of derivative

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Below you see the graph $f(x)=\frac{1}{2}x^2+3$ and the tangent line $l$ at the point $\rv{2,5.00000}$ .

generated image

Approximate the slope of $l$ at the point $\rv{2,5.00000}$ by calculating the difference quotient of $f$ at $2$ with difference $h$ for $h=1$ , $h=\frac{1}{10}$ , $h=\frac{1}{100}$ , $h=\frac{1}{1000}$ , and $h=\frac{1}{10000}$ , respectively. Give your answer to $5$ decimal places.

The difference quotient for $h=1$ is:

The difference quotient for $h=\frac{1}{10}$ is:

The difference quotient for $h=\frac{1}{100}$ is:

The difference quotient for $h=\frac{1}{1000}$ is:

The difference quotient for $h=\frac{1}{10000}$ is:

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