1. ## tangent & normal

what's exactly a rigorous definition of
tangent & normal to a curve suitable in all cases?

I know its a dumb qusetion but I have problems
in using it for concepts of calculus.

what's exactly a rigorous definition of
tangent & normal to a curve suitable in all cases?

I know its a dumb qusetion but I have problems
in using it for concepts of calculus.
the tangent line to a curve at a particular point gives the slope (rate of change) of the curve at that point. it is a straight line that touches the curve once in that vicinity. the normal line at the said point is the straight line that is perpendicular to the tangent line, and so cuts through the curve

3. ## ...another one

Thank you
A line can both be tangent & normal to a curve
but not to a function
isn't it true.

Thank you
A line can both be tangent & normal to a curve
but not to a function
isn't it true.
um, i don't think so. by definition the normal line is perpendicular to the tangent line. they can't be one and the same line

5. ## Tangent and Normal

Thank you
A line can both be tangent & normal to a curve
but not to a function
isn't it true.

In fact, there's nothing to stop a line being both a tangent and a normal to the same curve: it could be the tangent at one point, and normal to the curve at another point.

But perhaps that's not what you meant. So see the attachment, which shows the graph of the curve whose equation in polar coordinates is $\displaystyle r =\sin 2 \theta$. You'll see that each axis is both a tangent and a normal to the curve at the origin.

I'm not quite sure what you mean by
not to a function
This curve has a straightforward function that defines it.

6. Well a function has only one value of y defined for any "x" but a curve as in your attatchment can have many "y" for a single "x"
So I wanted to ask ,will that happen in both the cases which I don't think it will