## Integral of xcosx | How to Integrate xcosx dx

The integral of xcosx is equal to xsinx +cosx+C where C is an arbitrary constant, and it is denoted by ∫xcosx dx. The function xcosx is a product of two functions x and cosx. So we can use integration by parts formula to find its integration. Notation of Integral of xcosx: ∫xcosx dx Integration formula … Read more

## Limit of (x^n-a^n)/(x-a) as x approaches a: Formula, Proof

The limit of (x^n-a^n)/(x-a) as x approaches a is equal to nan-1. This limit is denoted by limx→a (xn-an)/(x-a), so the limit formula of (xn-an)/(x-a) when x tends to a is given as follows. limx→a (xn-an)/(x-a) = n⋅an-1 Lets prove this limit formula. Proof of limx→a (xn-an)/(x-a) To prove limx→a (xn-an)/(x-a) = n⋅an-1 we will consider three different cases … Read more

## Limit of (x^n-1)/(x-1) as x approaches 1

The limit of (x^n-1)/(x-1) as x approaches 1 is equal to n, that is, limx→1 (xn-1)/(x-1) = n. This follows from the formula limx→a (xn-an)/(x-a) = n⋅an-1 Put a=1, so we get that limx→1 $\dfrac{x^n-1}{x-1}$ = n. Let us now prove this limit formula. What is the Limit of (x^n-1)/(x-1) Answer: limx→1 (xn-1)/(x-1) is equal … Read more