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`y=f(x)=tan^(-1)((1-x^2)/(1+x^(2)))` <br> `tan^(-1)1-tan^(-1)x^(2)` <br> `=pi/4-tan^(-1)x^(2)` <br> Clearly, the domain of the function is R and `X^(2)ge0,AA x in R.` <br> Also function is even therefore the graph is symmetrical about the y-axis. <br> `tan^(-1)x^(2)ge0thereforetan^(-1) x^(2) in [0, pi/2)` <br> `therefore" "tan^(-1)x^(2) in (pi/2,0]` <br> `therefore" "pi/4-tan^(-1)x^(2) in(-pi/4,pi/4]` <br> Lets us first draw the graph for `xge0.` <br> `f(0)=pi/4-tan^(-1)0=pi/4` <br> Now if we increase the value of x from x=0, we find that the value of `x^(2)` increases, so the value of `tan^(-1)x^(2)` increases. Hence the value of `pi/4-tan^(-1)x^(2)` decreases. <br> When `x to, pi/4-tan^(-1)x^(2)topi/4-pi/2=pi/4` <br> Also when `pi/4-tan^(-1)x^(2)=0, tan^(-1)x^(2)=pi/4thereforex=1` <br> Thus, the graph intersects the x-axis at (1,0). <br> Thus, the graph of `f(x)" for x"le0` is as whown in the following figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C04_S01_012_S01.png" width="80%"> <br> Since f(x) is an even function, the graph is symmetrical about the y-xis, heance the graph of the function is as shown in the following figure. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_GRA_C04_S01_012_S02.png" width="80%"> <br> Here `f'(x) = 0 `0-0(2x)/(1+x^(2))`, therefore f(x) is differentiable at x = 0. <br> Also f"(x) `=2(x^(2)-1)/((1+x^(2))^(2))` <br> `f"(x) = 0 therefore x = +-1,` where the graph of f(x) changes its concavity. <br> For `x in (-1, 1), f"(x) lt0,` where tghe graph is concave downwards. <br> For `x in (-oo, -1)cup (1, oo), f"(x) lt0`, where the graph is convace upwards. Transcript

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00:00 - 00:59 | hello friends to as you can see in this question it is given that draw the graph of function Y = 26 equals to 10 inverse 1 - X square + 2 1st to differentiate This pass it here so when you differentiate this part we will get 1 upon 1 + 1 - x square upon 1 + x square ka whole square into into what minus 2 x square minus 2 then you will differentiate this part so why this part will get 1 - X square + x square ka whole square |

01:00 - 01:59 | when you go forward you will get your 1 upon 1 + 1 - x square upon 1 + x square is similarly into when you multiply after simplifying this - 4 X upon 1 + x square ka whole square and unique wait 800 because I want to find its from when you take this all part = 20 you will get - 4 x = 20 and from this you will get x = 20 so when a positive means the graph is increasing anode is negative its increasing as the value of effects will get 10 inverse 10 square upon 1 + 10 Square from this you will get tan inverse 1 and which is equals to 5 by 4 ok this part is equal to pi by 4 |

02:00 - 02:59 | now apply limit to Limit X tends to zero FX = to Limit X tends to infinity for Infinity and finding this is infinity Square One oneplus Infinity Square from this you will get Infinity upon Infinity vizinfinity only now when you put x tends to infinity hair effects equals to Limit X tends to infinity so here we will get 10 inverse 1 upon x square minus 1 upon 1 upon X square + 1 in this part at the place of 108 to put Infinity so here it is one upon Infinity square minus one upon an Infinity square + 1 and from this part you will get 10 inverse minus 1 upon 1 so it is it will |

03:00 - 03:59 | and this is -5.4 then the graph of this x square upon 1 + x square to it will be like this ok so this is my wife is this is my x-axis here it is per 14 and similarly produce -2 its gram would be like in drawing her the line crossing for minus power before because here at minus 5 by 4 and similarly I can draw it here and here it is crossing from 1 - 1 and hair from one how to close it will be like this |

04:00 - 04:59 | only this is a final graph of FX equal f x is equal to tan inverse 1 - x square upon 1 + |

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