3 years ago

There are 15 students going on a field trip. If 3/5 of them pack there lunches, how many students pack their lunches?

Mathematics

1 answer:

valentinak56 [21]3 years ago

6 0

Answer:

9 pack their lunches

Step-by-step explanation:

Take the number of students and multiply by the fraction that pack their lunches

15 *3/5 =

15/5 * 3

3*3

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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.

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