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

$ y = \dfrac{2x + 1}{x + 2} $, $ (1, 1) $

$y=\frac{1}{3} x+\frac{2}{3}$

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 7

Derivatives and Rates of Change

Limits

Derivatives

Tomas M.

October 4, 2020

Campbell University

Idaho State University

Boston College

Lectures

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04:51

01:52

there's a problem for eight of this tour. Calculus eighth edition Section two point seven Finding equation of the ten shilling to the curve At that given point, the curve is why cools the quantity to X one over the quantity X plus two and the point it's one one. Using the equation to the slope is m equals a limit has h birds zero of this function evaluated at a which is one plus a JJ. So everywhere there is an ex we end but one plus H one plus age minus the function evaluated at one. If we put this in here, you know, one times two plus one is three. In the nominated we have, I want us to his three. So this is a true victory for one and then a nominators. Tch! If we want to simplify this a bit in the numerator here simplifies to two plus two age plus one. That's two in a stream in the denominator here of this, uh, perfection. We have one plus H plus two that leaves just age of three minus one. Tried it by H to get rid of the denominator or the fraction in the numerator, We're gonna multiply with it denominator of that fraction. A triple screen. Ah, and what we can't as a simplified form is to age plus serene minus H minus three. Because we have minus one times its quantity, which is native one times H and negative one times three in the denominator, we have age times the quantity H plus three. Hey, we have now Ah, positive three in an industry in the numerator and to age minus age, which is just positive h And in the numerator and the denominator, there's one each. Each of those cancel. So we're left with the limited H of birches, zero of one over each pastry and his H purchase zero. This slope of perches acquired. He won over three or one third. We use point slope form to find the equation of detention line five minutes. Why one in closed M times x minus X one where Why one is one? Because our point is one one slip is one third and our X one is the one selling for why be it? Y equals one third x. I want her minus one times one negative one is equal to one third, and then we would think it was a negative one to the right. Since we're heading one on both sides, that leaves us with two thirds one minus one third. Oh, and this is our final answer for the equation of the tension line for this given function at the point one one.

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