Answer:
First term=1
Second term=-x
Third term=![2x^2](https://tex.z-dn.net/?f=2x%5E2)
Fourth term =![-\frac{28}{3!}x^3](https://tex.z-dn.net/?f=-%5Cfrac%7B28%7D%7B3%21%7Dx%5E3)
Step-by-step explanation:
We are given that function
![f(x)=(1+3x)^{-1/3}](https://tex.z-dn.net/?f=f%28x%29%3D%281%2B3x%29%5E%7B-1%2F3%7D)
We have to find the first four non zero terms of the Maclaurin series for the binomial.
Maclaurin series of function f(x) is given by
![f(x)=f(0)+f'(0)x+\frac{1}{2!}f''(0)x^2+\frac{1}{3!}f'''(0)x^3+....](https://tex.z-dn.net/?f=f%28x%29%3Df%280%29%2Bf%27%280%29x%2B%5Cfrac%7B1%7D%7B2%21%7Df%27%27%280%29x%5E2%2B%5Cfrac%7B1%7D%7B3%21%7Df%27%27%27%280%29x%5E3%2B....)
![f(0)=(1+3x)^{\frac{-1}{3}}=1](https://tex.z-dn.net/?f=f%280%29%3D%281%2B3x%29%5E%7B%5Cfrac%7B-1%7D%7B3%7D%7D%3D1)
![f'(x)=-\frac{1}{3}(1+3x)^{-\frac{4}{3}}(3)=-(1+3x)^{-\frac{4}{3}}](https://tex.z-dn.net/?f=f%27%28x%29%3D-%5Cfrac%7B1%7D%7B3%7D%281%2B3x%29%5E%7B-%5Cfrac%7B4%7D%7B3%7D%7D%283%29%3D-%281%2B3x%29%5E%7B-%5Cfrac%7B4%7D%7B3%7D%7D)
![f'(0)=-1](https://tex.z-dn.net/?f=f%27%280%29%3D-1)
![f''(x)=\frac{4}{3}\times 3 (1+3x)^{-\frac{7}{3}}](https://tex.z-dn.net/?f=f%27%27%28x%29%3D%5Cfrac%7B4%7D%7B3%7D%5Ctimes%203%20%281%2B3x%29%5E%7B-%5Cfrac%7B7%7D%7B3%7D%7D)
![f''(0)=4](https://tex.z-dn.net/?f=f%27%27%280%29%3D4)
![f'''(x)=-4\times \frac{7}{3}\times 3(1+3x)^{-\frac{10}{3}}](https://tex.z-dn.net/?f=f%27%27%27%28x%29%3D-4%5Ctimes%20%5Cfrac%7B7%7D%7B3%7D%5Ctimes%203%281%2B3x%29%5E%7B-%5Cfrac%7B10%7D%7B3%7D%7D)
![f'''(0)=-28](https://tex.z-dn.net/?f=f%27%27%27%280%29%3D-28)
Substitute the values we get
![(1+3x)^{-\frac{1}{3}}=1-x+\frac{4}{2!}x^2+\frac{-28}{3!}x^3+...](https://tex.z-dn.net/?f=%281%2B3x%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D1-x%2B%5Cfrac%7B4%7D%7B2%21%7Dx%5E2%2B%5Cfrac%7B-28%7D%7B3%21%7Dx%5E3%2B...)
![(1+3x)^{-\frac{1}{3}}=1-x+2x^2+\frac{-28}{3!}x^3+...](https://tex.z-dn.net/?f=%281%2B3x%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%3D1-x%2B2x%5E2%2B%5Cfrac%7B-28%7D%7B3%21%7Dx%5E3%2B...)
First term=1
Second term=-x
Third term=![2x^2](https://tex.z-dn.net/?f=2x%5E2)
Fourth term =![-\frac{28}{3!}x^3](https://tex.z-dn.net/?f=-%5Cfrac%7B28%7D%7B3%21%7Dx%5E3)
To find the surface area of any object, the first step that you must do is find all shapes that are present in the object.
Here we have 2 triangles and 3 rectangles.
Knowing this, simply find the area of each shape.
Since the triangles are the same, one is facing up and the other down, they both would be 15.6 cm^2.
The rectangles would be 54 cm^2. as there are 3 ( 6 x 3 cm) ones.
Add the values up to have the surface area.
It’s 85.2 cm^2.
<span>The
problem wants us to find the number that the 21% is 42.
42 is the 21% of 200
How:
=> 21% = 21 /100
=> .21
In order to get the answer we need to find a number to be multiplied by .21 and
get 42 as result.
=> 50 x .21 = 10.5
=> 100 x .21 = 21
=> 150 x .21 = 31.5
=> 200 x .21 = 42
thus, 42 is the 21% of 200.</span>