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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 knowledge of derivatives and the rules such as the product rule of derivatives and the quotient rule of derivatives. Expert Answer Given function: [y=x ln{ (x)}] For first derivative, […]

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. This question is based on the concept of directional derivatives. The directional derivative is the dot product of the gradient of the function with its unit vector. Expert Answer […]

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. Curvature is used for graphs which tells us how sharply a graph bends. Mathematically it is represented as: [K space= space || space frac{dT}{ds} space ||] Expert Answer We are given  the equation: […]

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 equations given at a specific point and product rule. Here we are going to find the second-order differential with the help of a reference point. Now, an ordinary differential equation also known as ODE is an […]

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 the binomial probability. This question uses the concept of the binomial distribution to find the binomial probability. In binomial distribution, we have the probability of two possible outcomes […]