Calculus: using Excel to verify limit nth root of n, n goes to infinity

Tutoring calculus, you cover limits. The tutor mentions using Excel for confirmation.

Because of Excel’s power, it can do some particular calculations you might use to verify a calculus limit.


In my April 19, 2016 post I develop the limit:


also known as the nth root of n as n approaches infinity.

Even when proven, sometimes there might be lingering doubt about a limit so hard to put in everyday context.

Worry no more – you can put it into context, using Excel. Check out the following verification calculations:



Clearly the limit of 1 is being approached as n increases.


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Home computer use: some practical experience with HP Notebook

For me, home computer use means self-tutoring. The tutor shares some experience with the HP Notebook.

When I can’t use the desktop, I often use a Notebook by HP, purchased last May, which runs Windows 10.

I had some problems with the HP Notebook early on, and had to restore it once. I was fearful it wouldn’t succeed, but it did, and worked better afterwards. We have our tensions sometimes, this HP Notebook and I, but they seem less and less.

Today, while I was watching a video on YouTube, the computer suddenly shut down. It turned back on, the screen telling me a problem had happened. It tried to start Windows, but was unsuccessful, so restarted, then tried again. As I recall, it still failed to start Windows, so restarted again.

A different screen appeared, telling me that Windows had failed to start the last time. It offered me two choices:

  1. an advanced system repair, or something similarly named, or
  2. try starting Windows again.

The last time I did a system repair, or restore, or what it might be called, it took a long time. “What can I lose,” I decided, “from just trying to start Windows one last time?” Therefore, that’s the option I chose – to attempt, once more, to restart Windows.

The computer did what I asked, and it worked: Windows did start successfully. A couple of minutes later I logged in like normal.

Although Windows was up and running, I didn’t assume all was well. A question mark icon called the HP Support Assistant is on the task bar. I clicked it, then Troubleshooting and Fixes, lower left on the HP Support Assistant screen.

Across the centre are two options I was happy to see: Performance Tune-up Check and Operating System Check. I first chose Performance Tune-up Check. As I recall, I had to give it permission to run. Then it offered me several checkbox choices, including System File Checker. “Great,” I thought. “That’s exactly what I need.”

When I chose to run System File Checker, I was warned that it could take an additional 30 minutes. I chose it anyway, and though it did take awhile, I could still watch videos, use Excel, etc, while it ran. It just worked in the background.

Eventually the Performance Tune-up Check, including the System File Checker, finished running and reported no problems. Next I clicked Operating System Check. It ran in the background as well. Later on, I looked back and found it had finished, reporting no issues.


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Math, engineering, trades: steepness measurement: definition of grade

Tutoring math, you encounter grade. The tutor discusses its definition and why it might be surprising.

Grade is defined as 100%*(vertical/horizontal). In the above diagram, it would be as follows:


By itself, rise/run is called slope.



What follows is a distinction that, to me, is important and interesting:

grade is not

rise/distance traveled

since, of course, you can’t drive along the horizontal course of a hill; rather, you can only drive on its surface.

At level, grade and (rise/distance traveled) are both zero. They remain virtually the same even at 20% grade, when (rise/distance traveled) is 19.6%. As the grade increases, however, they differ dramatically: at 100% grade, (rise/distance traveled) is 70.7%.

My interest in the difference between grade and (rise/distance traveled) is philosophical: why base a value on an indirect measurement (horizontal distance), when a direct measurement (distance traveled) is available?

In math, we use slope, of course; however, it’s usually in a context where actual measurements aren’t used. Rather, it’s just on paper.


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Lifestyle, Canadian brands: coffee: Best Gourmet Coffee Company, Kona Blend, ground

The tutor discusses more lifestyle self-tutoring: maintaining coffee quality when you’re living from a suitcase.

My wife says that my taste buds aren’t very refined – I can’t tell the difference between good food and great food. Likely, she tells a true story.

With coffee, however, we change roles: I’m the picky one, while she’s less discriminating. The truth is, I think I’m a discerning coffee connoisseur. Even though I drink two pots a day, if I can’t have a really good cup of coffee, I’ll usually pass altogether.

Having the coffee I appreciate is typically easy, since I’m a homebody: I just wait until the coffee I like is reasonable, then buy a lot. Good quality coffee is always reasonable, somewhere.

For freshness, beans have a distinct advantage over ground. At home, it’s convenient to grind the beans for each pot.

When you’re traveling, however, having tasty coffee isn’t necessarily so easy. Coffee needs to be drunk from porcelain, in my opinion, for the best flavour. Therefore, simply getting take-out coffee isn’t my best option, no matter how high-quality the coffee they serve.

Right now I’m living out of town, and have left my grinder at the workplace, along with the coffee pot I also brought down. Where I’m staying, I don’t have a grinder, but only a coffee maker. What to do?

My solution is to buy ground coffee, but to make sure I get good stuff. I don’t buy much ground coffee, so I’m not well educated about it.

Last night, at Country Grocer, I searched the shelves and found Kona Blend ground coffee, by the Best Gourmet Coffee Company. This morning I opened it and brewed some up.

I imagined some sort of foil peel-back closure. However, this coffee comes in a can; the only way I can figure to open it is with a can opener. (There happens to be one where I’m staying, but if you’re in a motel room or camping, you mightn’t have one.)

I brewed up a pot; I’m impressed. The flavour is agreeable, and I can taste the mellow sweetness of Kona. Being pre-ground, it’s not what I’d drink regularly at home, but for on the road, I recommend it. If I notice whole-bean coffee from Best Gourmet Coffee Company, I will definitely want to try it at home.

From the label, Best Gourmet Coffee Wholesalers, Ltd, is based in Maple Ridge, BC.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Mobile phones, electronics: should I unplug the phone charger when not in use?

Technology self-tutoring: the tutor checks the importance of unplugging an unused phone charger.

I’ve read in more than one place to unplug a phone charger when it’s not being used. Doing so I find inconvenient, but I’ve done it anyway because I’ve read I should. However, I’ve doubted there was a good reason.

Today I decided to research the matter.

howtogeek considers the potential power a plugged-in, but idle (and post 2012) phone or laptop charger will draw. However, the conclusion is that it’s negligible – barely worth the trouble of unplugging the charger after use. examines fire and short-circuit risk of a plugged-in, yet idle charger. The recommendation, short of unplugging the charger, is to use it in a power strip, in a well-ventilated, cool location, away from flammable materials. Then, even if left plugged while not charging, the risk of fire or short circuit is reduced.

Should you unplug the charger when not in use? You be the judge.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Driving: another strategy with Google maps

Driving in a different city means self-tutoring. The tutor tells a strategy.

Let’s imagine you need turn left onto a road, but don’t know how busy it will be. You might wish to do so from a light or a four-way stop to be sure of a chance to turn left safely.

I was in such a situation. Having driven the road already, I knew one street, at least, crossed it on a four-way stop. Which street was it?

Having a hunch, I entered the corner into Google search: Street A at Street B, City, Province.

A map appears from which you’re offered a street view. Clicking that and manipulating it, you can see if the corner is indeed a four-way stop.

Best of luck, fellow navigators:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Lifestyle: Mambo Gourmet Pizza, Nanaimo, BC.

Becoming familiar with a city means self-tutoring. The tutor discovers Mambo Gourmet Pizza, Nanaimo.

I’m based in Campbell River, but am working in Nanaimo for a couple of weeks. Times before, my wife has done the driving, etc. This time she stayed home, so I have to find my way around.

At lunchtime I went to find some food. Away from home, I often eat straight from a grocery store, but didn’t find one.

Along the sidewalk I passed Mambo Gourmet Pizza, noticing a couple of people eating inside. Half a block later I turned back, deciding to give Mambo a second look.

Entering, I could tell it’s a place that regular customers frequent. It’s warm and plain, with fresh pizzas on display at the counter.

I think a slice of pizza cost me $3.75. It was pretty large, but so good I decided halfway through that I’d get another one. After all, I had many hours left of instructing.

I’d say I was there for twelve minutes and two slices. Mambo Gourmet Pizza might be too good. Usually, I lose weight working away. This time, with Mambo just a few blocks away, I might end up gaining.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

Art: what is hue?

Tutoring web design, you might encounter other color systems besides rgb. The tutor begins about hue.

Hue exists on a scale from 0 to 360 degrees:

  • 0 is red
  • 120 is green
  • 240 is blue

Between those values are combinations of them: 30 degrees is orange, for instance, while 330 is hot pink.

Hue alone doesn’t constitute a color, because the color depends on the hue along with saturation and lightness (or intensity or value, depending on the system).

Hue-based color systems constitute a huge, complex topic to which I’ll be returning:)


Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

School supplies: the Five Star Pencil Pouch by Mead

Tutoring, you encounter school supplies. The tutor talks of one he recently adopted.

Let’s imagine the situation in which a person works in one place, not having to move their work or materials. Furthermore, let’s imagine they have their own workspace that they don’t share. That situation may not mandate using a pencil case.

If, on the other hand, the person needs to transfer their materials to and from work, or needs to store theirs among other peoples’, then they need to contain their pencils, pens, etc: a pencil case is probably indicated.

Needing to pack some school supplies for a trip, I went to a box where we store our kids’ old and new ones, looking for a pencil case. I found a Five Star Pencil Pouch by Mead.

The pouch’s bright colors – pink with other pastels – caught my attention, as did its binder rings. I get that fastening the pouch in a binder’s rings might be useful to prevent loss.

After a few minutes I noticed that the pouch has not just one zipper pocket, but two: one adjacent the rings, and the other opposite, facing outward. If the pouch is locked in a binder, you can access supplies from the outer pocket without flipping the binder open. Additionally, you can put pens in one pocket, pencils in the other, or so on. The second pocket is an organizational feature I admire.

The tag says ACCO Brands, of Dayton, Ohio, but mentions Hilroy as well. The name Mead appears on the pouch itself. Hilroy and Mead I’ve known forever.

I adopted the pencil pouch:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.