#1
Alright fellow UGers, I am currently learning in math how to use limits to find tangents. I am horribly confused. If someone could show me how to do the following question, I would be grateful

Find the slope of the tangent to the curve at the given point:

y = 1/x at (2,1/2)
using the formula -- (f(x) - f(a)) / x-a preferably plz

(the answer is -1/4 according to the back of the textbook)

thx in advanced

pepsi :liplickL
:
#2
Quote by pepsi_lovr
Alright fellow UGers, I am currently learning in math how to use limits to find tangents. I am horribly confused. If someone could show me how to do the following question, I would be grateful

Find the slope of the tangent to the curve at the given point:

y = 1/x at (2,1/2)
using the formula -- (f(x) - f(a)) / x-a preferably plz

(the answer is -1/4 according to the back of the textbook)

thx in advanced

pepsi :liplickL
:



Boy that really backfired eh?
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#3
u in alg. II?
cause i'm in geometry, and i don't think i know how to do that.
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#4
It's sad that I did this stuff in Calculus no less than a month and a half ago, and I can't remember how to do it.
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#5
Y=1/x
f(x)-f(a)/x-a
lim(xapp2) [(1/2)-(1/x)]/[x-2]
lim(xapp2)[(x-2)/2x]/[x-2]
simply fraction (x-2)/2x X -1/(x-2)
lim(xapp2)[-1/2x]
plug in limit. m=-1/4
#7
Quote by orangepaint
It's sad that I did this stuff in Calculus no less than a month and a half ago, and I can't remember how to do it.

agreed
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#8
Differentiation!

Two ways to do it. You might just find out that ( 1/(x+Δx) - x )/Δx approaches -1/x^2 as Δx approaches zero, and then sub 2 into -1/x^2, giving you -1/4, OR you could sub 2 in for x (but not Δx) at the top, giving you the same answer.

Your formula is dumb.
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