What is the limit as t approaches 0 of (sin(kt))/t ?

The limit as t approaches 0 of (sin(kt))/t is k

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limit as t approaches 0 of (sin(kt))/t

t \to 0 lim (\frac{sin ( k t )}{t})

k

Solution steps

t \to 0 lim (\frac{sin ( k t )}{t})

Apply L'Hopital's Rule

: t \to 0 lim (\frac{cos ( k t ) k}{1})

= t \to 0 lim (\frac{cos ( k t ) k}{1})

Plug in the value

t = 0

= \frac{cos ( k \cdot 0 ) k}{1}

Simplify

\frac{cos ( k \cdot 0 ) k}{1} : k

= k

f (x) = \frac{x}{a}

f (x) = x^{2} (4 - x)^{2}, at x = 1

\int_{0}^{1} \frac{1}{1 - x ^{2}} d x

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

\frac{\partial}{\partial x} (6 x^{2} + 7 y)

What is the limit as t approaches 0 of (sin(kt))/t ?
The limit as t approaches 0 of (sin(kt))/t is k