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Find nth Derivative of 1/(ax+b)

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The nth derivative of 1/(ax+b) is equal to (-1)nn!an/(ax+b)n+1. The nth derivative of 1/(ax+b) is denoted by $\dfrac{d^n}{dx^n}\left( \dfrac{1}{ax+b}\right)$ and its formula is given below: $\boxed{\dfrac{d^n}{dx^n}\left( \dfrac{1}{ax+b}\right)=\dfrac{(-1)^n n! a^n}{(ax+b)^{n+1}}}$ nth Derivative of 1/(ax+b) Question: What is the nth Derivative of $\dfrac{1}{ax+b}$? Answer: Let us put y = $\dfrac{1}{x+b}$ = (ax+b)-1. Using the power rule $\dfrac{d}{dx}\left( … Read more

What is the nth Derivative of x^n? [Solved]

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The nth derivative of xn is equal to n!. The nth derivative of x^n is denoted by $\frac{d^n}{dx^n}\left( x^n\right)$, and its formula is given as follows: $\boxed{\dfrac{d^n}{dx^n}\left( x^n\right)=n!}$ nth Derivative of xn Question: Find nth Derivative of xn. Answer: The nth derivative of x to the power n is obtained by repeatedly using the power … Read more

What is the nth Derivative of 1/x? [Solved]

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The nth derivative of 1/x is equal to (-1)nn!/xn+1. This is obtained by repeatedly using the power rule of differentiation. The nth derivative of 1/x is denoted by $\dfrac{d^n}{dx^n}\left( \dfrac{1}{x}\right)$, and its formula is given as follows: $\boxed{\dfrac{d^n}{dx^n}\left( \dfrac{1}{x}\right)=\dfrac{(-1)^n n!}{x^{n+1}}}$ nth Derivative of 1/x Question: How to find nth Derivative of 1/x? Answer: To find … Read more

Integral of xcosx | How to Integrate xcosx dx

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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

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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

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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

Limit of 1/x^2 as x approaches infinity

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The limit of 1/x^2 as x approaches infinity is equal to 0. As this limit is denoted by limx→∞ 1/x2, so the formula of the limit of 1/x2 is given as follows: limx→∞ 1/x2 = 0 What is the Limit of 1/x2 when x→∞ Answer: limx→∞ $\dfrac{1}{x^2}$ = 0. Explanation: As limx→∞ f(x)/g(x) is written as $\dfrac{\lim\limits_{x \to … Read more

Limit of x sin(1/x) as x approaches 0

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The limit of x sin(1/x) as x approaches 0 is equal to 0. This limit is denoted by limx→0 xsin(1/x). So the formula for the limit of x sin(1/x) when x tends to zero is as follows. limx→0 x sin(1/x) = 0. Let us now find the limit of xsin(1/x) using the Squeeze/Sandwich theorem. Proof … Read more

Limit of x^2 sin(1/x) as x approaches 0

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The limit of x^2 sin(1/x) as x approaches 0 is equal to 0, and it is denoted by limx→0 x2 sin(1/x) = 0. So the limit formula of x2 sin(1/x) when x tends to zero is given by limx→0 x2 sin(1/x) = 0. We will now find the limit of x2 sin(1/x) using the Sandwich/Squeeze … Read more

Limit of x^1/x as x approaches infinity

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The limit of x^1/x as x approaches infinity is equal to 1. This limit is denoted by limx→∞ x1/x, so the formula for the limit of x1/x when x tends to infinity is given by limx→∞ x1/x = 1. Let us now find the limit of x to the power 1/x when x tends to … Read more