Can someone plz explain ratio to me

2 answers:

7 0

A ratio shows how much of one thing there is compared to another. Ratios are usually written in the form a:b. If you are making orange squash and you mix one part orange to four parts water, then the ratio of orange to water will be 1:4 (1 to 4). The order in which a ratio is stated is important.

astra-53 [7]2 years ago

6 0

Meaning you don’t agree with what someone is saying other people will reply to you with either w or L. W is agreeing with you not agree with the thing you ratioed. L means they agree with the thing you ratioed

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Limit (sin4x-4sinx)/x^3 when x close to zero

BartSMP [9]

$\Large \boxed{\sf \bf \ \ \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}=-10 \ \ }$

Step-by-step explanation:

Hello, please consider the following.

Using Maclaurin series expansion, we can find an equivalent of sin(x) in the neighbourhood of 0.

$sin(x) \sim \left(x-\dfrac{x^3}{3!}\right)\\\\\text{So, in the neighbourhood of 0}\\\\\begin{aligned}(sin(4x)-4sin(x)) &\sim \left( 4x-\dfrac{(4x)^3}{3!}-4x+\dfrac{4x^3}{3!}\right)\\\\&\sim \left(\dfrac{x^3*4*(1-4^2)}{3*2}\right)\\\\&\sim \left(\dfrac{x^3*2*(-15)}{3}\right)\\\\&\sim \left(x^3*2*(-5)\right)\\\\&\sim \left(x^3*(-10)\right)\\\end{aligned}$