### Find the differential dy when y=rad(15+x^2).Evaluate dy for the given values of x and dx. x = 1, dx = −0.2

This article aims to find the differential of a given equation and the value of differential for given values of other parameters. Readers should know about differential equations and their basics to solve problems like in this article. A differential equation is defined as an equation contains one or more terms and the derivatives of one variable (i.e., the dependent variable) concerning another […]

### Evaluate the double integral. 4xy^2 dA, d is enclosed by x=0 and x=4−y^2 d.

In this question, we have to find the double Integration of the given function $4 x y^2$ by first integrating $x$, and then we will integrate the function with the given limits of $y$. The basic concept behind this question is the knowledge of double integration, limits of integration, and where […]

### Let F(x, y, z)=xi+yj+zk. Evaluate the integral of F along each of the following paths.

[c(t)=(t,t,t), space 0 le t le 3 space] The aim of this question is to find the Integration of the given function $F (x, y, z) =i+ yj +zk$ by first integrating $F (t, t, t)$ and then we will put the values of the limits given with the function. The basic concept behind […]

### Solve differential equation ty’+(t+1)y=t , y(ln2)=1 , t>0

In this question, we have to find the Integration of the given function $t y^prime + ( t + 1) y = t$ by using different integration rules. The basic concept behind this question is the knowledge of derivatives, integration, and the rules such as the product and quotient integration rules. Expert Answer […]

### Approximate the sum of the series correct to four decimal places.

[ boldsymbol{ sum_{ n }^{ infty } n = dfrac{ 1 ( -1 )^{ n } }{ 3^{ n } n ! } } ] This question aims to develop a basic understanding of summation expressions. A summation expression is a type of expression used to describe a series in a compact form. To find […]