(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the equation of the tangent line to the curve at the given point.

[tex]y = \sqrt{2x+1} , (4, 3)[/tex]

2. Relevant equations

a = 4

[tex]M =\lim_{x \to a} \frac{f(x) - f(a)}{x-a}[/tex]

or

[tex]Mpq = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}[/tex]

3. The attempt at a solution

[tex]M =\lim_{x \to 4} \frac{f(x) - f(4)}{x-a}[/tex]

[tex]M =\lim_{x \to 4} \frac{\sqrt{2x+1} - \sqrt{2 * 4 + 1}}{x-4}[/tex]

[tex]M =\lim_{x \to 4} \frac{\sqrt{2x+1} - 3}{x-4}[/tex]

[tex]M =\lim_{x \to 4} \frac{\sqrt{2x+1} - 3}{x-4} * \frac{\sqrt{2x+1} + 3}{\sqrt{2x+1} + 3}[/tex]

[tex]M =\lim_{x \to 4} \frac{2x - 3}{x-4(\sqrt{2x+1} + 3)}[/tex]

At this point I get stuck... I'm not sure what I can do from here. did I go wrong some where?

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# Homework Help: Find the equation of a tangent line to y=f(x)

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