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AravindG
 2 years ago
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
 2 years ago
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?

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UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1346418663569:dw

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@Callisto , @.Sam. , @eliassaab , @lgbasallote , @satellite73 , @mukushla

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1In 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

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1346418733121:dw

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i knw about tangent in circles ..my prob is i dont get idea on tangents of curves

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i cant draw tangent at a point if i am given a figure

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1346418814483:dw

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1346418835881:dw

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0perpendicular to what?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1346418935365:dw what is tangent at P?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Aravind  where the curve itself is flat (straight) the tangent coincides with it.

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0if it is coincidnt it will touch at more than one point!!

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Because the tangent to a straight i this straight line !

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0but tangent is defined to touch only at a point...err i am confused

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Yes it will "touch" at infinitely many points

amishra
 2 years ago
Best ResponseYou've already chosen the best response.0A 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
 2 years ago
Best ResponseYou've already chosen the best response.2yes , @Mikael the tangent is the flat line approximation of the curve

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0Through one given point in a curve, infinite tangents can be drawn. "is that true?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@Mikael read the qn agian Through one given point in a curve, infinite tangents can be drawn. "is that true?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0Through ONE given point in a curve, infinite tangents can be drawn. "is that true?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Read what @UnkleRhaukus said: this is the full definition: flat approximation

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i think the answer is 1

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1No  just one single welldefined tangent

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0yep :) only one tangent is allowed at point ryt?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2i can not think of any example where a curve could have more than one tangent

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1At point ON the curve YES "there can be only one" As Duncan McCloud says

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus i liked ur definition the tangent is the flat line approximation of the curve

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1It is not his (he would be lucky to be Isaac Newton, but he is unfortunately NOT)

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0those are newtons words??

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2it's not mine you say?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1I say that "tangent is a flat approximation to the curve" is ORIGINALLY Newton's definition.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2wow, where can i see that?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0"GREAT MINDS THINK ALIKE "

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1"Principia Mathematicae" (National Library, also the Library of the British Academy of Sciences

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Sorry  The Royal Academy od Sciences

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2we i havent read that one, ( i think its in latin)

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1I can get you a recent English Translation by a nobel prize winner (countrymanof Aravind originally...)

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0HMM..CAN u guys give me some real life situations where calculation of tangents is necessary?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1@UnkleRhaukus for a small fee naturally >;]

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah , Let\[f(x) = 33x^2 + 18x  15\] Find the tangent to this curve whose slope equals 99

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@Mikael i mean not that way

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2The only example i can think of where you could have multiple tangents is if they had som scale associated with them dw:1346419654145:dw

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0well i need real life example where calculation of tangent is necessary

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0for eg.space vehicle trajectory after it leaves earth

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Yes this is very much related to original problems Newton had to solve  instantaneous velocity

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2dw:1346419864709:dw

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Well  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

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1This will be solved by a tangent to exponential function graph

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus nic pic :P

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@Mikael do u have more?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2does it look like some athlete throwing a hammer ?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i thought someone was spinning thee bucket :P

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Yes  the typical (boring) school/colledge example would be:

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2instantaneous velocity or speed is the tangent of distance/time

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Let f(x) = (45x^2 33x + 7) sin (x5) . Find the approximate value at 5.01 using the linear approximation with its slope = derivative at x=5

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Btw @UnkleRhaukus did u open the picture I have attached above ?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0One last question which i gt stuck today : Find the equation of the tangent to the curve y=x7/((x2)(x3)) at the point where it cuts the x axis.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.2looks like 150$ i dont have @Mikael

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Let's show you the general idea to Find the equation of the tangent to the curve y=f(x) at the point x1

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0\[y=\frac{(x7)}{(x2)(x3)}\]

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.11. Find the point (in ur case the intersection with the axis)

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@Mikael i knw dat i done so many problems

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.12 Derivative at that point

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i cannot differentiate this coorectly

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i tred logarithmic differentiation

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Now you have THREE ( 3 ) data: (x, f(x)) and the slope=derivative

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Hey what the fuss it is simple Ratio function

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1\[(\frac{ f }{ g }) = \frac{ f'*g  f*g'}{ g^2}\]

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0now when i put in x=7 i am stuck

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1You did fine (beginning at least)

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Then do the formula above

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i think using quotient rule complicates the answer

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0what is wrong with my working

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Yes , but it GETS YOU THERE

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@UnkleRhaukus sharre ur view

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0my text says another method :

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i they havent shown how they gt it :(

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1WHAAT the f. ??? How did y get there  in the denumer ?

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Why not use simple and direct Ratio deriv. formula ??!

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0i dont knw can u fig out what the text has used ?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0@ash2326 , @myininaya PLS HELP

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Stop  you will awake all the evil spirits. It is a simple trick

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1When one applies the ratio formula one gets

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{ Polynom }{ ((x2)(x3))^2}\]

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Now as u notice in ur text's form the denomin is WITHOUT the square

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1They "transfered" one "sqrt of the denominator" as original y TO THE DENUMERATOR

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1In fact\[\frac{ 1*(x2)(x3)  (x7)*(Monomial ) }{(x2)^2(x3)^2} =\]

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0then how did 2x5 come?

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0wait i gt it !! 2x5 is differential of x^25x+6 !!

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1\[=\frac{ 1  (x7)*(Monomial) *((x2)(x3))^{1}}{ (x2)(x3)} \]

Rohangrr
 2 years ago
Best ResponseYou've already chosen the best response.1@AravindG Interact with this one : http://demonstrations.wolfram.com/TangentToACurve/

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1\[= \frac{ 1  Monomial*{Original Function} }{ (x2)(x3)} =\]

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1\[= \frac{ 1  y*Monomial }{ (x2)(x3) }\]

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0gt it !!! thx a lot!!!

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1I have given you a complete calculation

Mikael
 2 years ago
Best ResponseYou've already chosen the best response.1Close this question afterwards

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0my only doubt is why i didnt get it by logarithmic differentiation

AravindG
 2 years ago
Best ResponseYou've already chosen the best response.0closing thisone as page lagging
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