Corrections

[lookagain]

So you may think of the constant term in your function as -1/2*x^0, and then apply the Power Rule:

0*(-1/2)^(0-1)

See that multiplication by zero in front?

0*(-1/2)*x^(0-1) \(\displaystyle \ \ \ \ \ \ \ \ \) The x is still there. The (-1/2) is not being raised to (0-1).

 

[HallsofIvy]

0*(-1/2)*x^(0-1) \(\displaystyle \ \ \ \ \ \ \ \ \) The x is still there. The (-1/2) is not being raised to (0-1).

I'm not sure what your point is. Otis's point is that because of that "multiplication by zero in front", nothing else matters.

 

[Deleted member 4993]

I'm not sure what your point is. Otis's point is that because of that "multiplication by zero in front", nothing else matters.

I suppose LA is pointing out a typo in Otis's post (x is missing there).

 

[HallsofIvy]

Ah. Apparently Otis edited his post, to correct that, before I saw it.

 

[Otis]

Apparently Otis edited his post, to correct that, before I saw it.

Not so, says the timestamp. But, no matter; you and lookagain each made a valid point.

When reading an example of the Power Rule, students deserve to see a correct version.

And, once we note that some expression is multiplied by zero, none of the operations in that expression matter. It's like PEMDAS changes to M.

 

[Steven G]

I wasn't going to say anything but posters keep saying, to a calculus student!, that if one of the factors is 0 in an expression then the whole expression is 0. Come on, we all know better than to tell a student that. This would imply that if x=0 in x(1/x) the result is 0. What about with limits? So lim (x->0) (sin x)(1/x)= 0? After all, sin(0)=0.

 

[Otis]

I wasn't going to say anything but posters keep saying, to a calculus student!, that if one of the factors is 0 in an expression then the whole expression is 0. Come on, we all know better than to tell a student that. This would imply that if x=0 in x(1/x) the result is 0.

It's assumed that the expressions are defined. If x=0, then the expression 1/x is not defined.

Your example is similar to the classic trig-student mistake of claiming that an identity is false, after realizing that it doesn't hold for all values of the independent variable. They forget that -- even with identities -- we're working within a domain.

What about with limits? So lim (x->0) (sin x)(1/x)= 0? After all, sin(0)=0.

C'mon! You just made the classic calculus-student mistake with limits. In a limit statement where x approaches zero, x never takes on the value zero. You may make x as close to zero as you like, but x NEVER EQUALS ZERO.

As Denis would say, tattoo that on your wrist!!