Question

Limit as x-> 0 of (sin(x)/x) = 1

Answer 1

I have seen and understand the squeeze proof of this. But why when I use my calculator, find the value of sin(.00000000001)/.00000000001 (or any number zeros) do I get .01745 as the limit? I can't get any value larger than this.

Answer 2

you have to understand that calculators have limited precision. you need a more powerful calculutor to get a closer value.

Answer 3

Let me try some evaluation with mathematica - I will post the results I get.

Answer 4

If a TI-84 doesn't know the difference between .017 and 1 then all students are screwed.

Answer 5

@ehuman , it looks like you need to put your calculator into radians mode.

Answer 6

limit as x->0 (sin(x)/x) = 1 assumes x is in radians

Answer 7

thank you @inkyvoyd that fixed it. I had no idea that it could not be replicated in degree mode.

Answer 8

and thank you @phi

Answer 9

Always make sure your calculator is in radians mode for calculus. many a time have i spent hours wondering where I went wrong because my calculator input was right, only to finally realize that I was in degrees.

Answer 10

I got used to knowing when to go back and forth from degrees and radians while doing trig and precalc. there is a reason to need both. so in calc degree mode is not used or not used often?

@inkyvoyd

Answer 11

@ehuman I would not say I saw degrees mode in my calculus class after we finished our first few weeks of precalc review. The only time I found myself in degrees mode was when I was having trouble thinking in radians (I skipped trig class so I never spent time on the unit circle and stuff)