JEE ADVANCED 2024 PAPER 02 | FUNCTION | INTEGRARION | LIMIT

Let the function f : [1,∞)→𝑹 be defined by f(t)={█(〖(−𝟏)〗^(𝒏+𝟏) 𝟐, 𝒊𝒇 𝒕=𝟐𝒏−𝟏,𝒏∈𝐍@((𝟐𝒏+𝟏−𝒕))/𝟐 𝒇(𝟐𝒏−𝟏)+((𝒕−(𝟐𝒏−𝟏)))/𝟐 𝒇(𝟐𝒏+𝟏),𝒊𝒇 𝟐𝒏−𝟏𝒕𝟐𝒏+𝟏,𝒏∈𝐍)┤ Define g(x)=∫1_1^x▒〖𝑓(𝑡)𝑑𝑡,𝑥𝜖(1,∞).〗 𝐿𝑒𝑡 𝛼 𝑑𝑒𝑛𝑜𝑡𝑒𝑠 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑠𝑜𝑙𝑢𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 g(x)=0 in the interval ((1,8] and 𝛽=lim┬(x→1^+ )⁡〖(g(x))/(x−1)〗. Then the value of α+ β is equal to ___ JEE (ADVANCED) 2024 (PAPER 2) #math #maths #mathematics #education #science #learning #mathproblems #mathvideo #learnmath #mathtutorial #mathstricks #mathskills #mathlesson #calculus #geometry #permutation #combination #progression #series #ap #gp #binomialtheorem #limits #derivatives #aod #monotoniccurves #integration #definiteintegration #area #differentialequation #integrationbyparts #lineardifferentialequation #vector #3d #dotproduct #crossproduct #linein3d #planein3d #straightline #circle #parabola #ellipse #hyperbola #trigonometry #alliedangles #compoundangles #multipleangles #submultipleangles #itf #inversetrigonometry #logarithm #exponent #11thmath #12thmath #jeemains #jeeadvanced