answer:The Taylor expansion of a function f(x) around a point a is given by: f(x) = f(a) + f'(a)(x-a) + frac{f''(a)}{2!}(x-a)^2 + frac{f'''(a)}{3!}(x-a)^3 + cdots In this case, we have f(x) = tan^{-1}(2x) and a=3. First, we find the derivatives of f(x): f'(x) = frac{2}{1+(2x)^2} f''(x) = -frac{8}{(1+(2x)^2)^2} f'''(x) = frac{96x}{(1+(2x)^2)^3} Now, we evaluate these derivatives at x=3: f(3) = tan^{-1}(6) f'(3) = frac{2}{37} f''(3) = -frac{24}{1369} f'''(3) = frac{856}{151959} Substituting these values into the Taylor expansion formula, we get: tan^{-1}(2x) = tan^{-1}(6)+frac{2}{37}(x-3)-frac{24}{1369}(x-3)^2+frac{856}{151959}(x-3)^3 The answer is tan^{-1}(6)+frac{2}{37}(x-3)-frac{24}{1369}(x-3)^2+frac{856}{151959}(x-3)^3

answer:Given information: Future Value (FV) = 453 Number of years (N) = 8 Discount rate (I) = 14% To calculate the present value (PV), we can use the formula: PV = FV / (1 + I)^N Substituting the given values into the formula, we get: PV = 453 / (1 + 0.14)^8 PV = 453 / (2.71828)^8 PV = 453 / 6.2899 PV = 72.00 Therefore, the present value of 453 to be received in 8 years at a 14% annual discount rate is 72.00.

answer:The polygon's approximate interior angles are {0.56, 1.8, 0.78} radians, the area is 0.3 square units, and the perimeter is 2.85 units. This polygon is classified as 'Simple'.

answer:Murray code for teleprinter machines uses 5 bits. Therefore, the correct option is B) 5 bits.