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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?

Mathematics
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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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Other answers:

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i knw about tangent in circles ..my prob is i dont get idea on tangents of curves
i cant draw tangent at a point if i am given a figure
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perpendicular to what?
|dw:1346418935365:dw| what is tangent at P?
Aravind - where the curve itself is flat (straight) the tangent coincides with it.
@Mikael WHY???
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if it is coincidnt it will touch at more than one point!!
Because the tangent to a straight i this straight line !
but tangent is defined to touch only at a point...err i am confused
Yes it will "touch" at infinitely many points
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.
yes , @Mikael the tangent is the flat line approximation of the curve
Through one given point in a curve, infinite tangents can be drawn. "is that true?
No, no no
only one ryt?
Almost - two
????
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@Mikael read the qn agian Through one given point in a curve, infinite tangents can be drawn. "is that true?
Through ONE given point in a curve, infinite tangents can be drawn. "is that true?
Read what @UnkleRhaukus said: this is the full definition: flat approximation
i think the answer is 1
No - just one single well-defined tangent
yep :) only one tangent is allowed at point ryt?
i can not think of any example where a curve could have more than one tangent
At point ON the curve YES "there can be only one" As Duncan McCloud says
@UnkleRhaukus i liked ur definition the tangent is the flat line approximation of the curve
It is not his (he would be lucky to be Isaac Newton, but he is unfortunately NOT)
those are newtons words??
it's not mine you say?
I say that "tangent is a flat approximation to the curve" is ORIGINALLY Newton's definition.
wow, where can i see that?
"GREAT MINDS THINK ALIKE "
"Principia Mathematicae" (National Library, also the Library of the British Academy of Sciences
Sorry - The Royal Academy od Sciences
we i havent read that one, ( i think its in latin)
I can get you a recent English Translation by a nobel prize winner (countrymanof Aravind originally...)
HMM..CAN u guys give me some real life situations where calculation of tangents is necessary?
@UnkleRhaukus for a small fee naturally >;]
Yeah , Let\[f(x) = 33x^2 + 18x - 15\] Find the tangent to this curve whose slope equals 99
@Mikael i mean not that way
The only example i can think of where you could have multiple tangents is if they had som scale associated with them |dw:1346419654145:dw|
well i need real life example where calculation of tangent is necessary
for eg.space vehicle trajectory after it leaves earth
Yes this is very much related to original problems Newton had to solve - instantaneous velocity
more examples?
1 Attachment
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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
This will be solved by a tangent to exponential function graph
@UnkleRhaukus nic pic :P
@Mikael do u have more?
does it look like some athlete throwing a hammer ?
i thought someone was spinning thee bucket :P
Yes - the typical (boring) school/colledge example would be:
instantaneous velocity or speed is the tangent of distance/time
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
Btw @UnkleRhaukus did u open the picture I have attached above ?
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.
looks like 150$ i dont have @Mikael
help please
Let's show you the general idea to Find the equation of the tangent to the curve y=f(x) at the point x1
\[y=\frac{(x-7)}{(x-2)(x-3)}\]
1. Find the point (in ur case the intersection with the axis)
@Mikael i knw dat i done so many problems
2 Derivative at that point
i cannot differentiate this coorectly
i tred logarithmic differentiation
nt getting
Now you have THREE ( 3 ) data: (x, f(x)) and the slope=derivative
help please
Hey what the fuss it is simple Ratio function
i did like this
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\[(\frac{ f }{ g }) = \frac{ f'*g - f*g'}{ g^2}\]
now when i put in x=7 i am stuck
You did fine (beginning at least)
Then do the formula above
i think using quotient rule complicates the answer
what is wrong with my working
Yes , but it GETS YOU THERE
@UnkleRhaukus sharre ur view
my text says another method :
Which is ...?
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i they havent shown how they gt it :(
@Mimi can u help?
WHAAT the f. ??? How did y get there - in the denumer ?
ya i am also puzzled
Why not use simple and direct Ratio deriv. formula ??!
i dont knw can u fig out what the text has used ?
@ash2326 , @myininaya PLS HELP
Yes - Now i understand
HOW?
Stop - you will awake all the evil spirits. It is a simple trick
?
Lets start:
go on
When one applies the ratio formula one gets
.
\[\frac{ Polynom }{ ((x-2)(x-3))^2}\]
so?
Now as u notice in ur text's form the denomin is WITHOUT the square
yep how?
They "transfered" one "sqrt of the denominator" as original y TO THE DENUMERATOR
In fact\[\frac{ 1*(x-2)(x-3) - (x-7)*(Monomial ) }{(x-2)^2(x-3)^2} =\]
i see
then how did 2x-5 come?
wait i gt it !! 2x-5 is differential of x^2-5x+6 !!
\[=\frac{ 1 - (x-7)*(Monomial) *((x-2)(x-3))^{-1}}{ (x-2)(x-3)} \]
@AravindG Interact with this one : http://demonstrations.wolfram.com/TangentToACurve/
\[= \frac{ 1 - Monomial*{Original Function} }{ (x-2)(x-3)} =\]
\[= \frac{ 1 - y*Monomial }{ (x-2)(x-3) }\]
gt it !!! thx a lot!!!
I have given you a complete calculation
And thx is due
Close this question afterwards
i knw d rest
my only doubt is why i didnt get it by logarithmic differentiation
What does it mean ?
show u sas new qn
closing thisone as page lagging

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