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dollymixture219's avatar

Help on a difference quotient question?

Asked by dollymixture219 (18points) September 8th, 2012

f(t)=1/t-2, f(t)-f(1)/t-1, t not equal to1.

Can you explain to me how I work this out? I don’t know how you are supposed to figure it out when it’s not like f(x+h)-f(x)/h ?

Thanks for your help :)

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3 Answers

LostInParadise's avatar

This is just another way of expressing the limit of the slope at t = 1. It is the same as looking at [(1 + h) – f(1)] /h

f(1) = 1/(1 – 2) = -1
(f(t) – f(1)]/(t – 1) = [1/(t-2) + 1]/(t – 1) = [(t – 1)/(t – 2)]/(t – 1) = 1/(t – 2)
The limit as t approaches 1 is -1.

dollymixture219's avatar

So, I should leave my answer as 1/(t-2) then? The question asked me to leave the difference quotient in simplest form?

LostInParadise's avatar

Yes, that is what I would do

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