Question Number 104509 by bobhans last updated on 22/Jul/20

(1) (d^2 y/dx^2 ) −7 (dy/dx) +12y = 0  (2) y′′′−3y′′+4y′−2y= e^x −cos x  (3)y′′′+3y′′+5y′+3y=0  (4) lim_(x→0)  ((cot 4x−1)/(2x^2 ))

Answered by bramlex last updated on 22/Jul/20

(1) homogenous solution  λ^2 −7λ+12 = 0 ; λ=3, 4   ∴ y= C_1 e^(3x)  + C_2 e^(4x)    (4) lim_(x→0)  ((1−tan 4x)/(2x^2  tan 4x)) = ∞

Answered by Dwaipayan Shikari last updated on 22/Jul/20

lim_(x→0) ((1−tan4x)/(2x^2 tan4x))=((1−4x+((64x^3 )/3))/(2x^2 (x−(x^3 /3))))→∞