Lim x → 0 (tanx/x)^1/x^2 124323-Lim x- 0 (tanx/x)^(1/x^2)

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 Sample Paper Solutions Class 10 Maths Class 10 Science Class 10 English Class 10 Social Science Class 12 Maths Class 12 English Class 12 Accountancy Class 12 Economics To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW `lim_(x gt0) (tanx/x)^(1/x^2)`

Lim x- 0 (tanx/x)^(1/x^2)

Lim x- 0 (tanx/x)^(1/x^2)-As you can see this is an indeterminate form If you put value of x=1 it will be (0/0) form Use L'Hopital rule to solve this Differentiate the numerator and denominator separately till a validLimit from x→0 (1 tan x) / (1 sin x)^(x) = Checkout JEE MAINS 22 Question Paper Analysis Checkout JEE MAINS 22 Question Paper Analysis × Download Now

Limx 0 1 Sin X 1 Sin X Tan X Sarthaks Econnect Largest Online Education Community

7,556 solutions 1 0 cos 1 = 0 lim QUESTION Find each limit \lim _ {x \rightarrow 0} \frac {\tan ^ {1} x} {x} x→0 xan−1xApply L'Hospital's rule Tap for more steps lim x→02sec2(x)tan(x) lim x → 0 2 sec 2 ( x) tan ( x) Evaluate the limit Tap for more steps 2sec2(lim x→0x)⋅tan(lim x→0x) 2 sec 2 ( lim x → 0 x) ⋅ Note that 1 cos (x) = 2sin² (x/2) ⇒ lim x→0 xtan (x)/ 1 cos (x) = = lim x→0 xtan (x) / 2sin² (x/2) = = lim x→0 1/2 xtan (x) / sin² (x/2) / (x/2)² * (x/2)² Also, we know that lim x→0

 求lim(x→0)〔1cos2xtan^2 X〕/xsinx 当x趋向于0时，求1减cos2x加tanx的平方再除以x倍的sinx的极限值 当x趋向于0时，求1减cos2x加tanx的平方再除以x倍的sinx的极限值 展开 3X → 0 lim tan x c x → − 2 lim (− 4 p (x) 5 r (x)) / s (x) Limits of Average Rates of Change neous rates, limits of the form = (lim x → 0 (f (x) 7)) 2/3 lim x → 0 2 f (x) − lim x → 0 g (x) = (lim x →Expansion of tan x is, tan x = x 3 x 3 ⋯ Therefore required limit = x → 0 lim (1 3 x 2 ) 1 / x x → 0 lim (1 3 x 2 ) 3 / x 2 x / 3 = e 0 = 1, Here we have ignored higher order term

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 #lim_(x>0) (1cosx)/x^2 = lim_(x>0) (2sin^2(x/2))/x^2 = 1/2 lim_(x>0) (sin(x/2)/(x/2))^2 = 1/2# While the third function is continuous so #lim_(x>0) 1/cosx = 1/1 = 1#Correct option is A) Expansion of tanx is, tanx=x 3x 3⋯ Therefore required limit = x→0lim(1 3x 2)1/x 2 x→0lim(1 3x 2)3/x 21/3=e 1/3 , Here we have ignored higher order term Solve any

Incoming Term: lim x- 0 (tanx/x)^(1/x^2), lim x-0 x tan x/1-cos 2x, lim x mendekati 0 sin^2x-cos x+1/x tan x,