# Tutor.com Limits Session

##### May. 28, 2013

Session Transcript - Math - Calculus, 5/26/2013 11:22AM - Tutor.comSession Date: 5/26/2013 11:22AM
Length: 7.6 minute(s)
Subject: Math - Calculus

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[00:00:00] *** Please note: All sessions are recorded for quality control. ***

Travis (Customer)
[00:00:00] Find the limit

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[00:00:00] *** The student has 1124 minutes remaining. ***

Marcel V (Tutor)
[00:00:05] Hello, welcome to Tutor.com .
[00:00:13] Have you tried to work with it?

Travis (Customer)
[00:00:15] Hi
[00:00:16] yes
[00:00:24] but maybe what i was doing is too easy
[00:00:25] ?

Marcel V (Tutor)
[00:00:53] We can't cancel since they are adding or subtracting.
[00:00:59] Plus 1-cos t is inside sine
[00:01:04] So it is not something that is alone.

Travis (Customer)
[00:01:24] i was canceling the entire 1- cost
[00:01:28] not just the cost

Marcel V (Tutor)
[00:01:37] we can't leave sine alone either.
[00:01:44] 1-cos t is inside sine

Travis (Customer)
[00:01:53] doesnt' it just turninto 1?

Marcel V (Tutor)
[00:02:00] Yes it is just 1 but why?

Travis (Customer)
[00:02:12] sin1/1
[00:02:13] ?

Marcel V (Tutor)
[00:02:16] not at all

Travis (Customer)
[00:02:21] oppssorry
[00:02:28] how shall we proceed?

Marcel V (Tutor)
[00:02:31] sin(1)/1 is not 1 either.
[00:02:39] The idea is to remember the limit for sin(u)/u
[00:02:44] when u approaches to 0
[00:02:48] Do you remember that known limit?

Travis (Customer)
[00:02:54] yes
[00:02:57] very well

Marcel V (Tutor)
[00:03:03] So what is that equal to?

Travis (Customer)
[00:03:27] 1

Marcel V (Tutor)
[00:03:28] Right.
[00:03:34] And on the exercise what is u equal to?

Travis (Customer)
[00:03:49] u=1-cost

Marcel V (Tutor)
[00:03:56] Right.
[00:04:00] And when t approaches to 0
[00:04:05] we will have 1-1 so 0 for u
[00:04:35] So we can rewrite the limit as sin(u)/u
[00:04:38] and that is just 1.

Travis (Customer)
[00:04:54] ok cos(0)=1
[00:05:01] and we move the 1 to the other side = -1
[00:05:05] u=0

Marcel V (Tutor)
[00:05:16] well we had 1 - cos(t)
[00:05:22] so 1 - cos(0) is just 1-1

Travis (Customer)
[00:05:35] so sin0=0
[00:05:36] ?

Marcel V (Tutor)
[00:05:53] yes but that is not needed here.
[00:06:11] Is it clear why u approaches to 0 here when t approaches to 0?

Travis (Customer)
[00:06:32] so i have no idea what our final answer is?

Marcel V (Tutor)
[00:07:02] Everything is on board, so let's check the idea.

Travis (Customer)
[00:07:09] i'm going to take a wild guess here
[00:07:13] and say our final answer i
[00:07:15] is 1?

Marcel V (Tutor)
[00:07:18] We first have used u = 1-cost
[00:07:20] Yes it is just 1.
[00:07:30] So we can replace the exercise by sin(u)/u

Travis (Customer)
[00:07:31] ok than k you