Please help:
can u explain detailed what is a tangent to a curve .I know its a line just touching the curve at only one point but i need to understand it more and also would like to know how to draw the tangent if i am given any graph .Is THERE ONLY ONE tangent possible at a point?

- AravindG

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- UnkleRhaukus

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- AravindG

@Callisto , @.Sam. , @eliassaab , @lgbasallote , @satellite73 , @mukushla

- anonymous

In the general case the slope is computed by derivative.
But for circles - the straight line is PERPENDICULAR to the radius at the point of tangent

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## More answers

- UnkleRhaukus

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- AravindG

i knw about tangent in circles ..my prob is i dont get idea on tangents of curves

- AravindG

i cant draw tangent at a point if i am given a figure

- UnkleRhaukus

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- AravindG

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- UnkleRhaukus

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- AravindG

perpendicular to what?

- AravindG

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what is tangent at P?

- anonymous

Aravind - where the curve itself is flat (straight) the tangent coincides with it.

- AravindG

@Mikael WHY???

- anonymous

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- AravindG

if it is coincidnt it will touch at more than one point!!

- anonymous

Because the tangent to a straight i this straight line !

- AravindG

but tangent is defined to touch only at a point...err i am confused

- anonymous

Yes it will "touch" at infinitely many points

- anonymous

A tangent is a line outside the circle which touches only one point of the circle.
Through one given point, infinite tangents can be drawn.
A tangent at a given point is perpendicular to the radius of the circle.

- UnkleRhaukus

yes , @Mikael
the tangent is the flat line approximation of the curve

- AravindG

Through one given point in a curve, infinite tangents can be drawn. "is that true?

- anonymous

No, no no

- AravindG

only one ryt?

- anonymous

Almost - two

- AravindG

????

- anonymous

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- AravindG

@Mikael read the qn agian
Through one given point in a curve, infinite tangents can be drawn. "is that true?

- AravindG

Through ONE given point in a curve, infinite tangents can be drawn. "is that true?

- anonymous

Read what @UnkleRhaukus said: this is the full definition: flat approximation

- AravindG

i think the answer is 1

- anonymous

No - just one single well-defined tangent

- AravindG

yep :) only one tangent is allowed at point ryt?

- UnkleRhaukus

i can not think of any example where a curve could have more than one tangent

- anonymous

At point ON the curve YES "there can be only one" As Duncan McCloud says

- AravindG

@UnkleRhaukus i liked ur definition the tangent is the flat line approximation of the curve

- anonymous

It is not his (he would be lucky to be Isaac Newton, but he is unfortunately NOT)

- AravindG

those are newtons words??

- UnkleRhaukus

it's not mine you say?

- AravindG

@UnkleRhaukus ?

- anonymous

I say that "tangent is a flat approximation to the curve" is ORIGINALLY Newton's definition.

- UnkleRhaukus

wow, where can i see that?

- AravindG

"GREAT MINDS THINK ALIKE "

- anonymous

"Principia Mathematicae" (National Library, also the Library of the British Academy of Sciences

- anonymous

Sorry - The Royal Academy od Sciences

- UnkleRhaukus

we i havent read that one, ( i think its in latin)

- anonymous

I can get you a recent English Translation by a nobel prize winner (countrymanof Aravind originally...)

- AravindG

HMM..CAN u guys give me some real life situations where calculation of tangents is necessary?

- anonymous

@UnkleRhaukus for a small fee naturally >;]

- anonymous

Yeah , Let\[f(x) = 33x^2 + 18x - 15\]
Find the tangent to this curve whose slope equals 99

- AravindG

@Mikael i mean not that way

- UnkleRhaukus

The only example i can think of where you could have multiple tangents is if they had som scale associated with them
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- AravindG

well i need real life example where calculation of tangent is necessary

- AravindG

for eg.space vehicle trajectory after it leaves earth

- anonymous

Yes this is very much related to original problems Newton had to solve - instantaneous velocity

- AravindG

more examples?

- anonymous

##### 1 Attachment

- UnkleRhaukus

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- anonymous

Well - suppose Mr. Buffet has 23*10^9 $ in a hedge fund. Assume that his interest accumulates at 1% per second, draw the linear graph (straight line) approximating his wealth grouth after 27 seconds

- anonymous

This will be solved by a tangent to exponential function graph

- AravindG

@UnkleRhaukus nic pic :P

- AravindG

@Mikael do u have more?

- UnkleRhaukus

does it look like some athlete throwing a hammer ?

- AravindG

i thought someone was spinning thee bucket :P

- anonymous

Yes - the typical (boring) school/colledge example would be:

- UnkleRhaukus

instantaneous velocity or speed is the tangent of distance/time

- anonymous

Let f(x) = (45x^2 -33x + 7) sin (x-5) . Find the approximate value at 5.01 using the linear approximation with its slope = derivative at x=5

- anonymous

Btw @UnkleRhaukus did u open the picture I have attached above ?

- AravindG

One last question which i gt stuck today :
Find the equation of the tangent to the curve y=x-7/((x-2)(x-3)) at the point where it cuts the x axis.

- UnkleRhaukus

looks like 150$ i dont have @Mikael

- AravindG

help please

- anonymous

Let's show you the general idea to
Find the equation of the tangent to the curve y=f(x) at the point x1

- AravindG

\[y=\frac{(x-7)}{(x-2)(x-3)}\]

- anonymous

1. Find the point (in ur case the intersection with the axis)

- AravindG

@Mikael i knw dat i done so many problems

- anonymous

2 Derivative at that point

- AravindG

i cannot differentiate this coorectly

- AravindG

i tred logarithmic differentiation

- AravindG

nt getting

- anonymous

Now you have THREE ( 3 ) data:
(x, f(x)) and the slope=derivative

- AravindG

help please

- anonymous

Hey what the fuss it is simple Ratio function

- AravindG

i did like this

- AravindG

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- anonymous

\[(\frac{ f }{ g }) = \frac{ f'*g - f*g'}{ g^2}\]

- AravindG

now when i put in x=7 i am stuck

- anonymous

You did fine (beginning at least)

- anonymous

Then do the formula above

- AravindG

i think using quotient rule complicates the answer

- AravindG

what is wrong with my working

- anonymous

Yes , but it GETS YOU THERE

- AravindG

@UnkleRhaukus sharre ur view

- AravindG

my text says another method :

- anonymous

Which is ...?

- AravindG

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- AravindG

i they havent shown how they gt it :(

- AravindG

@Mimi can u help?

- anonymous

WHAAT the f. ??? How did y get there - in the denumer ?

- AravindG

ya i am also puzzled

- AravindG

@Mimi_x3

- anonymous

Why not use simple and direct Ratio deriv. formula ??!

- AravindG

i dont knw can u fig out what the text has used ?

- AravindG

@ash2326 , @myininaya PLS HELP

- anonymous

Yes - Now i understand

- AravindG

HOW?

- anonymous

Stop - you will awake all the evil spirits. It is a simple trick

- AravindG

?

- anonymous

Lets start:

- AravindG

go on

- anonymous

When one applies the ratio formula one gets

- UnkleRhaukus

.

- anonymous

\[\frac{ Polynom }{ ((x-2)(x-3))^2}\]

- AravindG

so?

- anonymous

Now as u notice in ur text's form the denomin is WITHOUT the square

- AravindG

yep how?

- anonymous

They "transfered" one "sqrt of the denominator" as original y TO THE DENUMERATOR

- anonymous

In fact\[\frac{ 1*(x-2)(x-3) - (x-7)*(Monomial ) }{(x-2)^2(x-3)^2} =\]

- AravindG

i see

- AravindG

then how did 2x-5 come?

- AravindG

wait i gt it !! 2x-5 is differential of x^2-5x+6 !!

- anonymous

\[=\frac{ 1 - (x-7)*(Monomial) *((x-2)(x-3))^{-1}}{ (x-2)(x-3)} \]

- anonymous

@AravindG Interact with this one : http://demonstrations.wolfram.com/TangentToACurve/

- anonymous

\[= \frac{ 1 - Monomial*{Original Function} }{ (x-2)(x-3)} =\]

- anonymous

\[= \frac{ 1 - y*Monomial }{ (x-2)(x-3) }\]

- AravindG

gt it !!! thx a lot!!!

- anonymous

I have given you a complete calculation

- anonymous

And thx is due

- anonymous

Close this question afterwards

- AravindG

i knw d rest

- AravindG

my only doubt is why i didnt get it by logarithmic differentiation

- anonymous

What does it mean ?

- AravindG

show u sas new qn

- AravindG

closing thisone as page lagging

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