While working on some probability question, I had to evaluate $\lim_{x \to \infty} \arctan(x)$. I knew the answer intuitively as $\pi/2$, yet I cannot figure out how to prove it by elementary means (without resorting to $\epsilon-\delta$ arguments).

Dec 21, 2020 · \(lim_{x \rightarrow \infty} \sec^{-1} (x)=\lim _{x \rightarrow \infty} \sec^{-1} (x )= \frac{\pi}{2} \). Example \(\PageIndex{1}\): Find \(\lim_{x \rightarrow \infty} sin\left( 2\tan^{-1}( x)\right)\).

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\lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx \int_{0}^{\pi}\sin(x)dx \sum_{n=0}^{\infty}\frac{3}{2^n} Show More

The \arctan function is the inverse function of \tan:\left(-\frac{\pi}2,\frac{\pi}2\right)\rightarrow\Bbb R and since this function is monotonically increasing then \lim_{x\to\frac\pi 2}\tan x=+\infty\iff \lim_{x\to+\infty}\arctan x=\frac\pi2

Oct 31, 2020 · Limit with arctan: $\lim_{x\rightarrow 0} \frac{x\sin 3x}{\arctan x^2}$ 0 Solve limit without use L'Hopital: $\lim _{x\to 0}\left(\frac{\sin\left(2x\right)-2\sin\left(x\right)}{x\cdot \arctan^2x}\right)$

Sep 28, 2017 · $$\lim _{x\to 0}\left(\frac{-\frac{2x}{\left(1+x\right)^2}+\sin\left(x\right)}{6x}\right)$$ So my answer is $\frac{1}{6}$, but the answer to the result using Wolfram Alpha is $-\frac{1}{6}$. What's wrong?

Feb 2, 2023 · In this video, I showed how evaluate the limit of arctan (x^2 + 1) as x goes to infinity using the shape of the graph.

Evaluate the limit of arctan(x) arctan (x) by plugging in 0 0 for x x. The exact value of arctan(0) arctan (0) is 0 0. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.

x → 1 lim (arctan (x)) Plug in the value x = 1 = arctan ( 1 ) Use the following trivial identity: arctan ( 1 ) = 4 π x 0 3 3 1 3 arctan ( x ) 0 6 π 4 π 3 π arctan ( x ) 0 ∘ 3 0 ∘ 4 5 ∘ 6 0 ∘ = 4 π