f(x)= array cl 1- ^3 x 3 ^2 x , & x 2 array . then =

Step-by-step solution

If f(x) is contineous at x= / 2 aligned & .L H L |_ x= / 2 = .R H L |_ x= / 2 =f ( 2 ) & L H L= _ x ⁻ 2 1- ^3 x 3 ^2 x aligned 0 0 form, using L-Hospital Rule _ x ⁻ 2 -3 ^2 x x -3(2 x) x = _ x ⁻ 2 x 2 = 1 2 f ( 2 )=L H L = 1 2 ...(i) R H L= _ x ⁺ 2 (1- x) ( -2 x)^2 = 1 2 Using L-Hospital Rule twice aligned & _ x ⁺ 2 (- x) 2( -2 x)(-2) = 1 2 & _ x ⁺ 2 x (-4)(-2) = 1 2 aligned aligned 8 & = 1 2 & =4 aligned = 1 2 4=2