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Contact [7]
3 years ago
13

Need help as fast as possible please

Mathematics
1 answer:
ankoles [38]3 years ago
4 0

Answer:

Correct Answer

Step-by-step explanation:

Mark as brainliest now NOW!

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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}

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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A bakery has 456 dozen cookies how many individual cookies are there
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The Garden Task
Igoryamba

If the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

  • the perimeter = 24 ft
  • the area = 36 sq. ft
  • if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
  • if the area of the garden is doubled, the area of the new garden = 72 sq. ft

<em><u>Recall</u></em>:

  • A square has equal side lengths
  • Perimeter of a square = 4(side length)
  • Area of a square = (side $ length)^2

<em><u>Given:</u></em>

Perimeter of square (P) = (14x - 32) $ ft

Side length (s) = (x + 2) $ ft

<em><u>First, let's find the </u></em><em><u>value of x</u></em><em><u> by creating an </u></em><em><u>equation </u></em><em><u>using the </u></em><em><u>perimeter </u></em><em><u>formula:</u></em>

  • Perimeter of a square = 4(side length)

  • Plug in the values

(14x - 32) = 4(x + 2)

  • Solve for x

14x - 32 = 4x + 8\\\\14x - 4x = 32 + 8\\\\10x = 40\\\\x = 4

<em><u>Find how much fencing would be needed (</u></em><em><u>Perimeter </u></em><em><u>of the fence):</u></em>

  • Perimeter of the fence = (14x - 32) $ ft

  • Plug in the value of x

Perimeter of the fence = 14(4) - 32 = 24 $ ft

<em><u>Find the </u></em><em><u>area </u></em><em><u>of the garden:</u></em>

  • Area of the garden = (side $ length)^2

Area = (x + 2)^2

  • Plug in the value of x

Area = (4 + 2)^2 = 6^2 = 36 $ ft^2

<u><em>Find the </em></u><u><em>perimeter </em></u><u><em>if the garden size is doubled:</em></u>

  • Perimeter of the new garden = 2 x 24 = 48 ft

<em><u>Find the </u></em><em><u>area </u></em><em><u>if the garden size is doubled:</u></em>

  • Perimeter of the new garden = 2 x 36 = 72 sq. ft

In summary, if the perimeter of the garden is (14x - 32) ft and has a side length of (x + 2) ft:

  • the perimeter = 24 ft
  • the area = 36 sq. ft
  • if the perimeter of the garden is doubled, the perimeter of the new garden = 48 ft
  • if the area of the garden is doubled, the area of the new garden = 72 sq. ft

Learn more here:

brainly.com/question/13511952

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B is your answer if you need me to explain why just ask me :) have a good day  
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