Aisha is analyzing the temperature readings of her science project over the last four days. What is $$\nabla^3y_3$$ in backward difference?

Tisha is conducting an experiment to determine the relationship between the temperature and the amount of ice melted. Using Lagrange’s interpolation formula, find $$y\left(x\right)$$ if $$y(0)=-12,\ y(1)=0,\ y(3)=12,\ y(4)=24$$

Sanya is studying the behavior of a certain function and has calculated the values $$y(0.1)=0.1003,\ y(0.15)=0.1511,\ y(0.20)=0.2027,\ y(0.25)=0.2553,\ y(0.3)=0.3093$$ for different inputs. She wants to find the fourth order forward difference column for these values. What is the result?

Rohan has a function $$y(1)=4,\ y(3)=12,\ y(4)=19,$$ and $$y(x)=7$$ find $$x$$ .

Find the area bounded by the curve and the x-axis from $$x=7.47$$ to $$x=7.52$$ by using Trapezoidal rule. Given that

$$f\left(7.47\right)=1.93,\ f\left(7.48\right)=1.95,\ f\left(7.49\right)=1.98,\ f\left(7.50\right)=2.01,\ f\left(7.51\right)=2.03,\ f\left(7.52\right)=2.06$$

A solid of revolution iss formed by rotating about the x-axis. The area between the x-axis, the lines $$x=0$$ and $$x=1$$ and a curve passing through the points $$\left(0,1\right),\ \left(0.25,\ 0.9896\right),\ \left(0.5,\ 0.9589\right),\ \left(0.75,\ 0.9089\right),\ \left(1,0.8415\right)$$ . Estimate the volume of the solid formed using Simpson's 1/3rd rule if volume $$V=\pi\ \int_0^1y^2dx$$

Evaluate $$y=\int_0^6f\left(x\right)dx\$$ using Simpson's 1/3rd rule and 3/8th rule given that $$y\left(0\right)=1,\ y\left(1\right)=0.5,\ y\left(2\right)=0.2,\ y\left(3\right)=0.1,\ y\left(4\right)=0.0588,\ y\left(5\right)=0.0385,\ y\left(6\right)=0.027$$

Which of the following is Unit 2?

Which of the following is/are the course outcomes with respect to Unit 2