write down in full the binomial expansion of (2-1/2x) rise to power 5 and simplify the coefficieng.(1) find the sum of the coefficient of x rise to power 3, x rise to power 4 and x rise to power 5 in the expansion.(2) use your expansion in (1) to calculate the value of (1.999) rise to power 5 correct your answer to 2singn figure.

Step-by-step explanation:

a) The full expansion of a binomial to the 5th power is ...

For the given binomial, a=2, b=-1/2x, so the expansion is ...

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b) The sum of coefficients of x^3, x^4 and x^5 is ...

  -5 +5/8 -1/32 = -4 13/32

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c) 1.999^5 = (2 -.001)^5 = (2 -0.002/2)^5

So, we can use the above expansion with x=.002. The result from part (b) tells us that the error from neglecting 3rd-power terms and higher will be on the order of 40×10^-9, far less than that necessary for the required accuracy.

  1.999^5 ≈ 32 -.002(40 -.002(20)) = 32 -.002(39.96) = 32 -0.07992

  1.999^5 ≈ 31.92

  = 32 (to 2 significant figures)

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.