What is the limit as x approaches pi/2 of-sin(x) ?

The limit as x approaches pi/2 of-sin(x) is -1

Popular >

limit as x approaches pi/2 of-sin(x)

x \to \frac{π}{2} lim (- sin (x))

- 1

Solution steps

x \to \frac{π}{2} lim (- sin (x))

Plug in the value

x = \frac{π}{2}

= - sin (\frac{π}{2})

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= - 1

x \to 0 + lim (\frac{1}{sin ( 2 x )})

x \to 2 lim (x^{4} + 3 x^{2} - x - 2)

x \to 3 lim (\frac{3 + x}{2 x - 6})

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

x \to 1 lim (3 x + 4)

What is the limit as x approaches pi/2 of-sin(x) ?
The limit as x approaches pi/2 of-sin(x) is -1