Math Is Fun Forum

kgh

Member

Registered: 2009-02-08

Posts: 11

Finding the slope of the tangent using limits

I am having a lot of difficulty with this question. I have tried for hours upon hours and even though I can get the answer using the derivative, I can't seem to get it using limits.

Here is the question:
Determine the slope of the tangent to the graph y=1/x at the general point whose x coordinate is a. Then, using the formula from part a), determine the slopes of the tangents to the graph at the points whose x coordinates are 1/4, 1/3, 1/2, 1 and 2.

I have to answer the question using the formula m=lim x->a f(x)-f(a)/x-a.

I would really really appreciate some help here! I think 1/x gets substituted for f(x), and then does 1/a get substituted for f(a)? Help!

Thanks!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Finding the slope of the tangent using limits

I have to answer the question using the formula m=lim x->a f(x)-f(a)/x-a.

Well, if you have to do it this way, then

kgh

Member

Registered: 2009-02-08

Posts: 11

Re: Finding the slope of the tangent using limits

I can't thank you enough! I was so close to having the answer, I just neglected to change a-x to -(x-a) in the numerator. I was just wondering, for part 2 of the problem...when x=1/4, for example, does that value get substituted for 1/x so the equation would be

1/4-1/a
--------
1/4-a

Thanks again!

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Finding the slope of the tangent using limits

is the slope of the tangent to the curve at

.

So when the

-coordinate is

. the slope is