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3 years ago

11

You are making fruit baskets using 54 apples 36 oranges and 73 bananas explain why you Cannot make identical fruit baskets witho

ut leftover fruit

1 answer:

Nady [450]3 years ago

4 0

Because 54, 36, and 73 don't have any common factors

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3 years ago

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dsp73

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2 years ago

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.

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

Then,

$\displaystyle \lim_{x\rightarrow0} \ {\dfrac{sin(4x)-4sin(x)}{x^3}}\\\\= \lim_{x\rightarrow0} \ {\dfrac{-10*x^3}{x^3}}\\\\=-10$

Thank you

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3 years ago

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What is the product of 76 and 6.0 x 10^2 expressed in scientific notation?

victus00 [196]

Answer: 676

Step-by-step explanation: 6.0 x 10^2=600 600+76=676

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3 years ago

What is the measure of x?

allsm [11]

My mother my mother

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3 years ago

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