# gradient of lines parallel to the y-axis

Discussion in 'Mathematics' started by fudgesweets, Jan 13, 2012.

1. ### fudgesweetsNew commenter

If you differentiate x=1 for example, what is the answer?

2. ### fudgesweetsNew commenter

If you differentiate x=1 for example, what is the answer?

3. ### PaulDGOccasional commenter

Differentiate with respect to what?

4. ### cyolba

It has a gradient of inifinity (which doesn't exist) of course!

cyolba, opening a whole can of worms

5. ### SC00BY

x=1
Diff x wrt y gives
dx/dy=0
and use chain rule
dy/dx=1/(dx/dy)
gives dy/dx=1/0
which gives the required result.

6. ### Maths_MikeNew commenter

The x axis has gradient 0. The y axis has gradient 1/0 (as above.)
The product of the gradients of 2 perpendicular lines is -1

1\0 x 0 = -1

7. ### emilyisobel

Michael - that is naughty - behave!

8. ### Maths_MikeNew commenter

Sry - bit of a sense of humour failure!

9. ### SC00BY

Yes, both 0/0 and 0 to the power 0 are classed as indeterminate values since they can be shown to take any value. For example limit as x tends to 3 of (x squared -9)/(x-3) tends to 0/0 but also tends to the value of 6. Using similar arguments you can shown that 0/0 tends to any value you choose.