Summer Calc

[turtleness]

I'm having trouble with some problems with factorials that I've never seen anything like before. Can someone please go through these step by step?
Say if the statement is true or false:
2x # x (is the # a typo?)

(1/x)!x

Factor:
x^2(x!1)! 4(x!1)

Simplify:
(5(x+h)^3! 5x^3)/h

 

[mmm4444bot]

true or false:

2x # x (is the # a typo?)

(1/x)!x

The first expression above does not look like a true/false exercise, to me. It's likely an error, as they apparently did not give you any definition for symbol #.

I see no instructions for the second expression above. (Again, it does not look like a true/false question.) It can be simplified; try letting x = 2, 3, 4, and write it all out. Look for a pattern, when cancelling the factor of x to the right of the factorial.

Factor:

x^2(x!1)! 4(x!1)


Simplify:

(5(x+h)^3! 5x^3)/h

In the first expression above, I do not recognize the notation x!1. Do you know what they intend?

The second expression above does look like it contains a typographical error. If we replace the ! symbol with a subtraction symbol, the resulting expression will be a "difference quotient". Difference quotients are common in introductory calculus courses and precalculus courses.

[5(x + h)^3 - 5x^3]/h

If you expand the numerator, there will be some factors of h that can be factored out of the numerator to cancel with the h in the denominator.

On the rest, I would contact the instructor. :cool:

 

[HallsofIvy]

I suspect that you are not telling us the whole problem. It happens, sometimes, that, to make sure you understand a general property of "operators", they will define a new operator such as, for example, "x#y= x(y+1)" and then ask questions about that operator.

Are you sure these problems are about factorials? In "x^2(x!1)! 4(x!1)" it looks to me like "!" is being used as a binary operator, operating on both "x" and "1" rather than just x.

(And, although it is not required, "x" is usually used for real number variables, "n" for integers. And the factorial is only defined for positive integers.)

 

[turtleness]

This is honestly all it said. It's a worksheet that just lists off problems with "Simplify" or "Say if it's true or false" above it. There are no other directions. That's why I'm so lost on it

 

[mmm4444bot]

From where does this worksheet come?