 ### Find yʹ and yʹʹ. y=xln(x)

In this question, we have to find the first and second derivatives of the given function y=x ln(x) The basic concept behind this question is the

### Suppose you are climbing a hill whose shape is given by the equation z=100 – 0.05x^2 – 0.1y^2, where x,y and z are measured in meters, and you are standing at a point with coordinates (60, 50, 1100). The positive x-axis points east and the positive y-axis points north. If you walk due south, will you start to ascend or descend? At what rate?

The question aims to find the direction if the person starts to walk to the south, whether the person will ascend or descend, and at what rate.

### Find the curvature of r(t) = 7t, t2, t3 at the point (7, 1, 1).

This question aims to find the curvature of the given equation for the points (7,1,1).This question uses the concept of calculus and curvature.

### If xy + 3ey = 3e, find the value of y” at the point where x = 0.

This problem aims to familiarize us with higher-order differential equations. The concept required to solve this problem is ordinary differential

### Consider a binomial experiment with n=20 and p=0.70.

Find f(12). Find f(16). Find $P(x ge 16)$. Find $P(x le 15)$. Find $E(x)$. Find $var(x)$ and $sigma$. The main objective of this question is to find