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# tangent line diff. quotient value plugin.

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I just need help pluggin in the values. I never did ones with values outside of the sqr.

Veteran  Apr 24, 2017
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#1
+4164
+3

This is just the plugging in part...

$$g(x) = 5-\sqrt{4-x}$$

To find g(3 + h), replace every instance of x with (3 + h) .

$$g(3+h) = 5-\sqrt{4-(3+h)} \\g(3+h) =5-\sqrt{4-3-h} \\g(3+h) = 5-\sqrt{1-h}$$

To find g(3), replace every insance of x with 3.

$$g(3) = 5-\sqrt{4-3} \\g(3) =5-\sqrt{1} \\ g(3) =4$$

So

$$m_{tan}=\lim_{h\rightarrow 0} \frac{g(3+h)-g(3)}{h} =\lim_{h\rightarrow 0} \frac{(5-\sqrt{1-h})-(4)}{h} \\~\\=\lim_{h\rightarrow 0} \frac{1-\sqrt{1-h}}{h}$$

Then you gotta actually evaluate the limit and all that to get the slope of the line when x = 3

hectictar  Apr 24, 2017
#2
+223
+1

okay thanks alot guy.

Veteran  Apr 25, 2017

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