Question

Is the limit here 1? Seems like a confusing problem.

Answer 1

http://prntscr.com/cg6fpf

Answer 2

No, a slope shouldn't be necessary. The thing is that the graph goes straight through 1 for an interval like this:

Answer 3

Just fill it in then check for any tapering (like 0.0182, 0.00135...) trends with the slope.

You need to calculate slope between each of those points and the original proposed point... sorry, I just started learning about this

Answer 4

Is this single var or multi var?

Answer 5

Must be single variable, this is the first Calculus class I've taken

Answer 6

Hm.

I've never done a problem like this that didn't involve secant/tangential slope for limits.

Answer 7

As far as I know, the closest one to your question that I've worked on involved graphing and then drawing your own tangent line, from which you pick two points and calculate the slope from that

Answer 8

two points that are on the graph as well, of course

Answer 9

In this section the problems have never involved slope. We're expected to look at how the function changes as x approaches c. Probably I should try substituting the given values in the equation.

Answer 10

Maybe. I don't know what stuff/format your professor teaches in, so I don't want to give you the wrong idea/direction.

Sorry

Answer 11

using radian mode (not degree mode)
use a calculator to figure out the value, and fill in the table.

Answer 12

Why radian mode?

Answer 13

because dividing (sin x) by x requires "dimensionless" units i.e. radians
it is one of the main reasons we use radians, so we can "mix" trig and algebra

Answer 14

Okay...I'll try it out

Answer 15

The values I got are -0.99335, -0.99993, -1, 1, 0.99993, and 0.99335

Answer 16

how do you get negative numbers. you should be raising it the the 4th power
(sin(x) / x)^4

Answer 17

They're all supposed to be positive

Answer 18

for 0.001 I get
0.999999333

but I think it's clear we are approaching 0.999999..... or 1

Answer 19

Must be a calculator mistake. Tried again, your answer is right. But yes, the numbers are approaching 1.

Answer 20

which makes sense, because limit x->0 of sinx /x is 1
and raising it to the 4th power, it is still 1