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

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

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limit as x approaches 0 of cos(x)-x

x \to 0 lim (cos (x) - x)

1

Solution steps

x \to 0 lim (cos (x) - x)

Plug in the value

x = 0

= cos (0) - 0

Simplify

cos (0) - 0 : 1

= 1

x \to 0 + lim ((x + cos (x))^{\frac{4}{x}})

x \to 0 lim (3^{x + 1} - 3)

x \to - \frac{π}{2} lim (- 5 x - \frac{π}{2})

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

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

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