promath The limit of cos(1/x) as x approaches infinity is equal to 1. The limx→∞ cos(1/x) formula is given as follows: $\lim\limits_{x \to \infty} \cos \big(\dfrac{1}{x} \big)=1$. In this post, we will learn how to prove the limit of cos(1/x) when x tends to ∞. Limx→∞ cos(1/x) Question: What is the limit of cos(1/x) when x … Read more
The limit of (1+1/n)^n as n approaches infinity is equal to e. The limn→∞ (1+1/n)n formula is given by $\lim\limits_{n \to \infty} \big(1+\dfrac{1}{n} \big)^n=e$. That is, the limit of (1+1/x)x when x→∞ is equal to e. In this post, we will learn to prove the limit of log(1+x)/x when x tends to zero. Limn→∞ (1 … Read more
The limit of sin(√x)/x as x approaches 0 DOES NOT exist, that is, the limx→0 sin(\sqrt{x})/x formula is given by $\lim\limits_{x \to 0} \dfrac{\sin \sqrt{x}}{x}=$ not exist. Let us learn how to find the limit of sin root x divided by x when x tends to 0. Find Limit of sin(√x)/x when x→0 We have … Read more
The limit of sin(x^2)/x as x approaches 0 is equal to 0. The limx -> 0 sin(x2)/x formula is given by $\lim\limits_{x \to 0} \dfrac{\sin x^2}{x}=0$. Let us learn how to find the limit of sin x square divided by x when x tends to 0. Limx → 0 sin(x2)/x We have $\lim\limits_{x \to 0} … Read more
The limit of (a^x-1)/x as x approaches 0 is equal to 1. The limx -> 0 (ax-1)/x formula is given by $\lim\limits_{x \to 0} \dfrac{a^x-1}{x}=\ln a$ where ln a = logea. In this post, we will learn to prove the limit of (ax-1)/x when x tends to zero. Limx → 0 (ax -1)/x Prove that … Read more
The limit of log(1+x)/x as x approaches 0 is equal to 1. The limx -> 0 (log(1 + x))/x formula is given by $\lim\limits_{x \to 0} \dfrac{\log(1+x)}{x}=1$. In this post, we will learn to prove the limit of log(1+x)/x when x tends to zero. Limx → 0 log(1 + x)/x Prove that limx → 0 … Read more
The integral of 1/x^n (1 by x power n) is equal to x-n+1/(1-n) +C. Here we will learn how to integrate 1/xn using the power rule of integration. The integration formula of 1/xn is given by $\int \dfrac{dx}{x^n}=\dfrac{x^{1-n}}{1-n}+C$ where C denotes an integral constant. Integration of 1/xn The integral of 1/xn is denoted by ∫dx/xn. … Read more
The derivative of 1/xn (1 by x power n) is equal to -n/xn+1. Here we learn how to find the derivative of 1 divided by x to the n. The derivative formula of 1/x^n is given by $\dfrac{d}{dx} \big( \dfrac{1}{x^n}\big) = -\dfrac{n}{x^{n+1}}$. Derivative of 1/xn Answer: The derivative of 1/xn is equal to -n/xn+1. Explanation: … Read more
The integral of root cotx is equal to ∫√cotx dx = $-\dfrac{1}{\sqrt{2}}$ tan-1 ($\dfrac{\cot x-1}{\sqrt{2\cot x}}$) – $\dfrac{1}{2\sqrt{2}}$ log $|\dfrac{\cot x+1-\sqrt{2\cot x}}{\cot x+1+\sqrt{2\cot x}}|$ +C where C is an arbitrary integral constant. Here we will learn how to integrate square root of cotx. Integral of √cotx Question: Find ∫√cotx dx. Solution: Let cotx=t2. Differentiating w.r.t … Read more
The integration of root tanx + root cotx is equal to √2sin-1(sinx−cosx)+C. Here we learn how to integrate √tanx+√cotx. The integral formula of $\sqrt{\tan x}+\sqrt{\cot x}$ is given by $\int (\sqrt{\tan x}+\sqrt{\cot x}) dx$ = $\sqrt{2}\sin^{-1}(\sin x -\cos x)+C$. Find ∫(√tanx+√cotx) dx $\int (\sqrt{\tan x}+\sqrt{\cot x}) dx$ = $\int \Big(\dfrac{\sqrt{\sin x}}{\sqrt{\cos x}}+\dfrac{\sqrt{\cos x}}{\sqrt{\sin x}} \Big) … Read more