limit of tangent as x approaches pi 2 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
Hint Write tan x dfrac sin x cos x and then take the limit lim x to large frac pi 2 dfrac sin x cos x The numerator approaches 1 and the denominator The limit of arctan x as x to infty is pi 2 Maybe I don t understand the arctan enough because by looking at the graph I see that indeed it approaches pi But why
limit of tangent as x approaches pi 2
limit of tangent as x approaches pi 2
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Limit Of Arctan Function As X Approaches Infinity Limits At Infinity
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As x 2 tanx Since arctanx is the inverse function of tanx 2 Limits at infinity are used to describe the behavior of a function as the input to the function becomes very large Specifically the limit at infinity of a function f x is the value that the
Evaluate the limit of x by plugging in 2 for x Simplify the answer Tap for more steps The result can be shown in multiple forms Free math problem solver answers your algebra Enter the limit you want to find into the editor or submit the example problem The Limit Calculator supports find a limit as x approaches any number including infinity The calculator
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What is the limit as x approaches pi 2 of tan x The limit as x approaches pi 2 of tan x is diverges The tangent function x has an infinite number of vertical asymptotes as x therefore it does not approach a finite limit nor does it approach as
First lets substitute t frac x 4 as suggested before lim limits x to infty arctan frac x 4 lim limits t to infty arctan t t frac x 4 X 2 x msquare log msquare sqrt square nthroot msquare square le ge frac msquare msquare cdot div x circ pi left square right frac d dx
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limit of tangent as x approaches pi 2 - Tan x approaches infinity as x approaches pi 2 because tan x sin x cos x and cos x approaches zero as x approaches pi 2 Tan is opposite over adjacent in a right triangle So if