1 Answer

Ajinzrathod · Answer 1 · 2021-12-18T09:48:03+0000

Answer:

108

Explanation:

So the slope of the tangent line to the graph of y=4x² is:

$\lim_(x \to 3) (4x^3-108)/(x-3)$

As directed, try values near 3 to estimate the slope. So, using a calculator, I'm going to try 2.9, 2.99, and 2.999:

2.9:

$(4(2.9)^3-108)/((2.9)-3)\approx104.44$

2.99:

$(4(2.99)^3-108)/((2.99)-3)\approx107.6404$

2.999:

$(4(2.999)^3-108)/((2.999)-3)\approx107.96$

And let's also try 2.9999 and 2.99999. So:

$(4(2.9999)^3-108)/((2.9999)-3)\approx107.9964$

And:

$(4(2.9999)^3-108)/((2.9999)-3)\approx107.99964$

Let's also check by coming from the right with 3.001:

$(4(3.001)^3-108)/((3.001)-3)\approx108.036$

Therefore, our limit or slope is:

$\lim_(x \to 3) (4x^3-108)/(x-3)\approx108$

And we're done!

The answer is 108

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