What is the limit as x approaches 0 of (cos(x))/(96) ?

The limit as x approaches 0 of (cos(x))/(96) is 1/96

limit as x approaches 0 of (cos(x))/(96)

x \to 0 lim (\frac{cos ( x )}{96})

\frac{1}{96}

Decimal

0.01041 \dots

Solution steps

x \to 0 lim (\frac{cos ( x )}{96})

Plug in the value

x = 0

= \frac{cos ( 0 )}{96}

Use the following trivial identity:

cos (0) = 1

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{96}

\frac{d y}{d t} + 0.3 t y = 9 t

l a pl a ce t r an s f or m 6 t - 3

l a pl a ce t r an s f or m t^{2} + e^{- 2 t} sin (3 t)

x \to 0 + lim (e^{(\frac{1}{x})})

d er i v a t i v e \frac{y ^{2} - 2}{2 y ^{2}}

What is the limit as x approaches 0 of (cos(x))/(96) ?
The limit as x approaches 0 of (cos(x))/(96) is 1/96