lim tan3x 2x 3x sin 2x

lim tan3x 2x 3x sin 2x Limits a foundational tool in calculus are used to determine whether a function or sequence approaches a fixed value as its argument or index approaches a given point Limits can be defined for discrete sequences functions of one or more real valued arguments or complex valued functions

Solution We have lim x 0 tan 3x 2x 3x sin2 x It becomes 0 0 form Taking x common from numerator and denominator lim x 0 x tan 3x x 2 x 3 sin2 x x lim x 0 tan 3x x 2 3 sin x x sin x lim x 0 3 tan 3x 3x 2 3 sin x x sin The Limit Calculator is an essential online tool designed to compute limits of functions efficiently Here s how to use it Begin by entering the mathematical function for which you want to compute the limit into the above input field or scanning the problem with your camera

lim tan3x 2x 3x sin 2x

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lim tan3x 2x 3x sin 2x
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Find The Limit As X Approaches 0 Of sin 3x sin 2x YouTube
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lim-xto0-sin2x-3x-2x-tan3x

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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 will use the best method available so try out a lot of different types of problems Hint lim x to 0 frac sin x x lim x to 0 frac tan x x 1 Rewrite your expression as frac tan 3x x cdot frac x sin 2x frac 32 cdot frac tan 3x 3x cdot frac 2x sin 2x

Thus the limit of sin 3x cot 2x sin 3 x cot 2 x as x x approaches 0 0 from the right is 1 5 1 5 1 5 Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor Using tan A B frac tan A tan B 1 tan A tan B twice we obtain tan 2x frac 2 tan x 1 tan 2 x tan 3x frac 3 tan x tan 3 x 1 3 tan 2 x so that frac tan 2x tan 3x frac 2 1 3 tan 2 x 3 tan 2 x 1 tan 2 x

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Explanation lim x 0 tan 3x sin 2x Using L H pital s rule lim x 0 d tan 3x dx d sin 2x dx lim x 0 3sec2 3x 2cos 2x lim x 0 3 2sec3 3x 3 2 Therefore so goes the original limit lim x 0 tan 3x sin 2x 3 2 Answer link Hence frac sin 2x tan 3x sim 0 frac 2x 3x frac23 which proves the limit is dfrac23

Limits Calculator online with solution and steps Detailed step by step solutions to your Limits problems with our math solver and online calculator lim x 0 9x 2 sin 3x 3x 1 cos 3x 2 0 Note that tan 3x sin 3x cos 3x and lim x 0 sinx x 1

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lim tan3x 2x 3x sin 2x - Thus the limit of sin 3x cot 2x sin 3 x cot 2 x as x x approaches 0 0 from the right is 1 5 1 5 1 5 Free math problem solver answers your algebra geometry trigonometry calculus and statistics homework questions with step by step explanations just like a math tutor