Evaluate the following limits LHopitales Rule lim x rightarr

Evaluate the following limits (L\'Hopitales Rule) lim x rightarrow infinity 1 - cosx/x2; lim x rightarrow 0 x/tan-1(4x) lim x rightarrow infinity x2 - 1/x2 - x; lim x rightarrow 0 x - sin x/x - tan x lim x rightarrow 0 x2 - sin(x)/x + sin x ; lim x rightarrow infinity (x + 1/x)x lim x rightarrow infinity 2x3 + 15x2 + 2x + 10/e3x + 5x; lim x rightarrow 0 + x3 ln x lim x rightarrow infinity 8e2x + 5ex + 1/e3x + 15ex + 23; lim x rightarrow infinity 2x - 3x/3x - 4x

Solution

a. f(x) = sinx/2x = 0 f(x) = x ( 1 + 16x)^2 = 0 b. 2x/2x-1 = 1 c. 1 -cosx/1 - sec^2x = sinx/2sec^2x tanx = 1/2 do the following for the other parts too