This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems: 9. Use the first 3 terms in the expansion of sqrt(4-3x) to approximate sqrt(4.03) to 3 decimal places. Step 1: Relate sqrt(4-3x) to sqrt(4.03). We need 4-3x = 4.03. -3x = 4.03 - 4 -3x = 0.03 x = (0.03)/(-3) x = -0.01 Step 2: Write sqrt(4-3x) in the form (a+b)^n. sqrt(4-3x) = (4-3x)^1/2 Here, a=4, b=-3x, and n=(1)/(2). Step 3: Expand using the binomial theorem (a+b)^n = a^n + n a^n-1b + (n(n-1))/(2!) a^n-2b^2 + The first three terms are: Term 1: a^n = 4^1/2 = 2 Term 2: $n a^n-1b = (1)/(2) (4)^1/2 - 1 (-3x) = (1)/(2) (4)^-1/2 (-3x) = (1)/(2) · (1)/(sqrt(4)) (-3x) = (1)/(2) · 12