According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
An acceptable result cannot be found manually for it requires a <em>high</em> number of elements, with the help of a solver we find that the <em>approximate</em> value of √3 is 1.732.
<h3>How to approximate the value of a irrational number by binomial theorem</h3>
Binomial theorem offers a formula to find the <em>analytical</em> form of the power of a binomial of the form (a + b)ⁿ:
(1)
Where:
- a, b - Constants of the binomial.
- n - Grade of the power binomial.
- k - Index of the k-th element of the power binomial.
If we know that a = 1, b = 2 and n = 1 / 2, then an approximate expression for the square root is:
√3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...
To learn more on binomial expansions: brainly.com/question/12249986
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You have the following function:

Derivate implictly the previous expression, as follow:

Where you have used that:

Then, the implicit derivative of the given expression is:

Next, solve for y' as follow:

Answer:
x<1
Step-by-step explanation:
You would just subtract 5 from both sides of the equation. The sign does not flip because you are not multiplying or dividing any negative number across the sign. So simply x+5 (-5) < 6 (-5). On the left side the 5 would cancel out. on the other side 6-5 is equal to 1.
Answer: x<1
Answer:
4 different ways
Step-by-step explanation:
Total number of children = 4
Distribution of the 4 children :
Number of boys = 3 ; Number of girls = 1
Boy = B ; Girl = G
Possible combinations :
BBBG ; GBBB ; BBGB ; BGBB
From the pascal triangle number of e; number of outcomes = 2
Having exactly 3 boys and 1 girl
Hence, of any of the 4 four total children, 3 must be boys and 1 girl ;