To derive euler’s method, we truncated the taylor series expansion of yi+1 at the linear term. we could truncate at the quadratic term instead, giving the so-called taylor method of order 2. this method approximates yi+1 byωi+1= ωi+ hf(ti,ωi) + h^2/2. df/dt| (ti,ωi)a. for the ivp y'(t)= y^2. e^-t, 0 ≤ t ≤ 1, y(0)= 1, calculate df/dt. b. by hand, use both euler's method and the taylor method of order 2 to approximate y(1) with h=0.5

Select all the correct answers.natalie buys a new car. in the first month, the odometer on the car records 800 miles. from past experience, she expects to drive 900 miles per monthselect all the functions that can be used to find the number of miles, f(n), recorded on the odometer after n months.of(n) = 800n + 100f(n) = 9001 - 100f(n) = 900n + 800(1) = 800; }(n) = f(n - 1) + 900, for n > 2f(1) = 800; 1(n) = f(n − 1) + 100, for n > 2(1) = 900; }(n) = f(n - 1) + 800, for n > 2

Two positive integers are 3 units apart on a number line. their product is 108. which equation can be used to solve for m, the greater integer? m(m – 3) = 108 m(m + 3) = 108 (m + 3)(m – 3) = 108 (m – 12)(m – 9) = 108

Astudent has created the give circuit diagram. it consists of a battery, a resistor, and a light bulb. in one minute, 1.2c of charge flows through the resistor. how much charge flows through the light bulb in one minute?