promath The limit of (1+1/x)^x as x approaches infinity is equal to e. Here we will discuss Lim x→∞ (1+(1/x))^x formula with proof. Note that Limx → ∞ (1+$\frac{1}{x}$)x = e. Limx→∞ (1+(1/x))x Formula with Proof The formula of limx→∞ (1+(1/x))x is given by limx → ∞ (1+(1/x))x =e. Explanation: Let y = limx→∞ (1+$\frac{1}{x}$)x. So … Read more
The limit of cosx/x as x approaches 0 does NOT exist. That is, limx→0 (cos x)/x is undefined. $\lim\limits_{x \to 0} \dfrac{\cos x}{x}$ = NOT exist. Let us now show that the limit of (cos x)/x when x tends to 0 does not exist. Limx→0 (cos x)/x Question: What is the limit of cosx/x when … Read more
The limit of cosx/x as x approaches infinity is equal to 0. The formula of limx→∞ (cos x)/x is given below: $\lim\limits_{x \to \infty} \dfrac{\cos x}{x}=0$. Here we find the limit of (cos x)/x when x tends to infinity. Limx→∞ (cos x)/x = 0 Proof Question: What is the limit of cosx/x when x tends … Read more
The integral of 1 is equal to x+C where C is a constant. The integration of 1 is denoted by ∫1 dx, and its formula is given as follows: ∫1 dx = x+C where C is an arbitrary integration constant. Here we will learn how to integrate 1. Integration of 1 Question: What is the … Read more
The integral of 0 is equal to C where C is an arbitrary constant. The integration of 0 is denoted by ∫0 dx, and its formula is given by ∫0 dx = C where C is an integration constant. In this post, we will learn how to integrate the constant 0. NOTE: We know that … Read more
The integral of 1/x^2 is equal to -1/x +C where C is a constant. The integration formula of 1/x2 is as follows: $\int \dfrac{1}{x^2} dx = -\dfrac{1}{x}$ +C. In this post, we will learn how to integrate 1/x^2. Integration of 1/x2 Answer: The integration of 1/x2 is equal to -1/x +C. Explanation: Step 1: Using … Read more
The integral of x^2 (x square) is equal to x3/3+C where C is a constant. The integration formula of x2 (x square) is given by ∫x2 dx = $\dfrac{x^3}{3}$ +C. Let us now learn how to integrate x^2 dx. Integration of x2 Answer: The integral of x square is ∫x2 dx = x3/3+C. Explanation: To … Read more
The integral of 1/2x (1 by 2x) is equal to 1/2 ln|x|+C where C denotes an integration constant. Here we learn how to integrate 1/2x. The integration of 1/2x formula is given by $\int \dfrac{1}{2x} dx=\dfrac{1}{2}\ln |x|+C$. Integration of 1/2x Answer: The integration of 1/2x is 1/2 ln|x|+C. Explanation: We need to find the integral … Read more
The derivative of cot2x is equal to -2cosec22x. The differentiation of cot2x is denoted by d/dx (cot2x), and its formula is given by $\dfrac{d}{dx}$ (cot 2x) = -2cosec22x. cot2x Derivative Answer: The derivative of cot2x, that is, d/dx(cot2x) is equal to -2cosec22x. Explanation: To find the derivative of cot2x by the chain rule, let us … Read more
The integral of ln2x is equal to x(ln2x−1)+C where C is a constant. Here, we will learn how to integrate ln2x. The integration of ln(2x) is given as follows: ∫ln2x dx = x(ln2x−1)+C Integration of ln2x Question: What is the integration of ln2x? Solution: To find the integration of ln2x, we will use the integration … Read more