11What was you?
How many times do 2x and x2+1 intersect and what r the points of intersection? I will tell reason for this question later :)
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20 Answers
1are yaar...koi baat nahi.......x2 wale graph ko y axis pe higher kar do by 1.......n plot it..u will get the points........u can find the third point by plotting the graph dude...on a big paper..just try i guess u can plot it.....just shift mah x2 grph above by +1 on y axis..n u will get x2+1.
11How will find out third point?
P.S
Graph shd b between 2x and x2+1
1thin graph is 2x............even i wwas quite shocked wen i plotted the graphs n found that there are 3 points....one is in -ve side.......anoder is 2[that was easy....2x and x2] are both 22 here............and the third intersection is between x=4 and 8 sumwhere......just try plotting till 5 .u will understand...........
1I think 3..., x=0 and x=1.. the other one i will try later :P
The slopes show that they must meet 3 times...
11In a test I took here, i got this question and gave the ans as two (u can't expect me to draw the graph to scale!!) as 0 and 1 were the only solutions I could think of. Well, thanks everybody :))
1Applying numerical technique (which you guys will learn in IIT), the third root comes out to be 4.2575
1Slope of x2+1 = 2x.
Slope of 2x = 2xloge2.
At x=1, slope of x2+1 > 2x.... so x2 + 1 is steeper and on the inside.
so seeing the values of 2xloge2 > 2x for higher numbers then they must meet at another point.
I think the another point is around x=4.5
33By slope he means check slope of slope of both curves at x=1
and limit of slope of 2x-(x2+1) as x→+∞
You will understand.
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11what do u mean "The slopes show that they must meet 3 times" ?
1yes , at three points
x=0
x=1 and the other point cannot be calculated exactly