Question 1

At 1:20 you verify that you're in radian mode. Why do you need to be in radian mode versus degrees?

Accepted Answer

I think what is being asked is how can we tell from the question that we need to use radians. We could do this by checking the other values in the function and we would clearly see that the measurements are not in degrees. I do not see anywhere that the problem clearly states that the solution needs to be in radians, however the information used to provide the solution makes it clear we are talking about radians.

Question 2

okay what happens if approaching from both sides we dont get the same value ?

Accepted Answer

A limit *does not exist* if the *left side limit is not equal to the right side limit*.

Question 3

One of the problems given to me during this section is estimating the limit as x approaches "f(x)=sin(x)ln(x)"
I am not sure what ln(x) is or how to input it on a calculator.
Conventional wisdom tells me that is "Function of X equals Sine of X times Line of X", but that would be f(x)=sin(x)*x which does not accurately graph the given answers.
Any assistance?

Accepted Answer

ln stands for the natural logarithm.  
It is the logrithm with base e.

e is an irrational number like pi approximately equal to 2.71828

Question 4

Is it possible to calculate such things without using a calculator within a reasonable time? Or is it almost impossible?

Accepted Answer

If you don't use a calculator for calculating sin(x) or cos(x) you'll need a trig table -- that's what people used before calculators were invented. There's really no advantage to using a trig table that I can see. So you pretty much have to use a calculator for sin(x) and cos(x). The rest you might be able to do by hand in a reasonable amount of time, but there's really no reason to.

Question 5

How come when I'm in radian mode in a calculator,and when I need to input 1.0001 into 1/In(x)-1/x-1,how come I get something like 99985.124328663 instead of something like 0.9999932534?Whenever I try this,it always happens.IT'S DRIVING ME CRAZY!Can someone help me?

Accepted Answer

You need to use parentheses to indicate what belongs in the denominator or elsewhere.

Question 6

How can you do these by hand

Accepted Answer

You will learn how to do that as you advance in the course. There are mathematical ways to get the exact limit (if it exists) by direct means, not by estimations. But, you need to understand the concept of a limit before moving onto that material (and it eventually gets very advanced).

Question 7

How do you get a graphical calculator on your computer or iPads?

Accepted Answer

A popular one is available at this website: https://www.desmos.com/calculator

Question 8

In the exercise after this video I came across the problem: f(t) = t^6-1/t^3+1. All had been well and good until this one, as the values in the table disagreed with what my calculator told me. For instance, in the table, when  t= -1.01, f(t) = −2.030301, but my calculator told me otherwise, and so did just working it out by hand. (By hand I mean with the aid of a non-graphing calculator).
Here's a link to the calculator I used, for your convience with -1.001 already plugged in: https://www.desmos.com/calculator/quctv6lflq

Accepted Answer

Your answer is correct.   You may have had a problem with the calculator misinterpreting what you meant if you did not use parentheses.
Here's the computation:
( t⁶-1)/(t³+1)
= (t³-1)(t³+1)/(t³+1)
= (t³-1),  where t ≠ -1
plugging in t=-1.01
= (-1.01)³ - 1
= -1.030301 - 1
= -2.030301

Question 9

Why is it important to know whether x is approaching to 0 from positive or not? then, if x is approaching 0 from negative is the x->0^ - underneath limit?

Accepted Answer

Consider the equation `x/|x|`. Everything to the right of x=0 will give you the answer 1, but everything to the left of x=0 will give you -1. So, the limit as x approaches zero is one if you approach from positive and -1 if you approach from negative, but if you don't specify which side you're approaching from, then the limit doesn't exist. It's important to specify which side you're approaching from if the limit on either side will be different.

Question 10

Unfortunately, the university I attend does not allow for the use of any calculators on exams in Calculus. Any advice on how to do homework? Should I or should I not use a calculator? The graphing calculator helps with visualization and long division and multiplication take a very long time to write out and such and converting decimals to fractions... huge numbers when you start dealing with ∆y/∆x

Accepted Answer

You just need to make sure you know the material well enough to do the work efficiently without a calculator. You need to be able to easily spot singularities, asymptotes, vertices, end behavior, etc.  
 
You should also know squares of all integers at the very least through 25. You should know the cubes at least through 10.  And you should be able to do this whether you're allowed a calculator or not.

For example, when you see ∜1250 you should easily see that is 5∜2 because you know that 5⁴ = 625 and 625*2 = 1250.
  
I took this subject quite a long time ago, before even the best calculators would have been of much help anyway. It isn't easy material, of course, but I honestly think your university has a point in not allowing the calculator on the exams. The calculators have become so advanced that one of the better models could solve a problem you had no idea how to solve -- we don't need to have scientists and engineers who don't know what the math means and do the math their jobs require, but who just got through university by using a really good calculator.

Calculus, all content (2017 edition)

Course: Calculus, all content (2017 edition) > Unit 1

One-sided limits from tables

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