What is the limit as x approaches pi of x+cos(x) ?

The limit as x approaches pi of x+cos(x) is pi-1

limit as x approaches pi of x+cos(x)

x \to π lim (x + cos (x))

π - 1

Decimal

2.14159 \dots

Solution steps

x \to π lim (x + cos (x))

Plug in the value

x = π

= π + cos (π)

Use the following trivial identity:

cos (π) = (- 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}

= π - 1

d er i v a t i v e \frac{8 x ^{7}}{5 y ^{4}}

in v erse l a pl a ce \frac{1}{s \cdot ( s + 1 ) ^{2}}

d er i v a t i v e 9^{x}

\int \frac{sin ^{2} ( θ )}{cos ( θ )} d θ

x \to 5 lim (x^{2} + 24)

What is the limit as x approaches pi of x+cos(x) ?
The limit as x approaches pi of x+cos(x) is pi-1