What is the limit as x approaches 0 of (4x-sin(x))/x ?

The limit as x approaches 0 of (4x-sin(x))/x is 3

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limit as x approaches 0 of (4x-sin(x))/x

x \to 0 lim (\frac{4 x - sin ( x )}{x})

3

Solution steps

x \to 0 lim (\frac{4 x - sin ( x )}{x})

Divide by highest denominator power:

4 - \frac{sin ( x )}{x}

= x \to 0 lim (4 - \frac{sin ( x )}{x})

x \to a lim [f (x) \pm g (x)] = x \to a lim f (x) \pm x \to a lim g (x)

With the exception of indeterminate form

= x \to 0 lim (4) - x \to 0 lim (\frac{sin ( x )}{x})

x \to 0 lim (4) = 4

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

= 4 - 1

Simplify

= 3

\int e^{y} y^{2} d y

\frac{\partial}{\partial x} (9 x e^{x + y})

y^{^{''}} + 4 y^{^{'}} + 5 y = - 5 x + 5 e^{- x}

\int \frac{3}{2} e^{2 x} d x

x y^{^{'}} + y = y^{2}, y (1) = - 5

What is the limit as x approaches 0 of (4x-sin(x))/x ?
The limit as x approaches 0 of (4x-sin(x))/x is 3