Question

lim x tends to 0 (sin 3x/x)=?

Answer 1

hellooooo
here is yours ans

limit of xtends to 0 sin3x/x

on multiply and divide it with 3

3×sin3x/3x

3(1)=3. {{{sin3x/3x=1}}}

Answer 2

$\displaystyle \sf \: \lim_{x \to 0} \frac{sin \: 3x}{x} = 3$

Given :

$\displaystyle \sf \: \lim_{x \to 0} \frac{sin \: 3x}{x}$

To find :

The value of the limit

Formula :

$\displaystyle \sf{ \lim_{x \to 0} \frac{sin \: x}{x} = 1 }$

Solution :

Step 1 of 2 :

Write down the given limit

Here the given limit is

$\displaystyle \sf \: \lim_{x \to 0} \frac{sin \: 3x}{x}$

Step 2 of 2 :

Find the value of the limit

$\displaystyle \sf \: \lim_{x \to 0} \frac{sin \: 3x}{x}$

$\displaystyle \sf = 3 \times \: \lim_{x \to 0} \frac{sin \: 3x}{3x}$

Let u = 3x

So that x → 0 gives u → 0

Then above becomes

$\displaystyle \sf = 3 \times \: \lim_{u \to 0} \frac{sin \: u}{u}$

$\displaystyle \sf = 3 \times 1\: \: \: \: \bigg[ \because \:\lim_{x\to 0} \frac{sin \: x}{x} = 1 \bigg]$

$\sf = 3$

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