Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

Limit x tends to 0 [tanx/x]^1/x^2 is ? lim m tends to infinity [cos (x/m)] ^m is? I need the procedure of solving these sums.. Thank you

Limit x tends to 0 [tanx/x]^1/x^2 is ?
lim m tends to infinity [cos (x/m)] ^m is?
I need the procedure of solving these sums.. Thank you

Grade:12

5 Answers

Har Simrat Singh
42 Points
8 years ago

In These sums put yhe value of x like in first question tanx/x when x tens 0 is 1 and i/x2 becomes infinity ie it is of the form 1 raised to the infinity

a simple formula is Lt x tends 0 f(x)^g(x) where it is of the form 1^inf is equal to e^Lt x tends 0 ((f(x) -1)/G(x))

for first it becomes e^ ( lt x tends 0 tanx -x/x^3)

apply L hopital twice it becomes e^1/3sec^2x tanx/x

= e^1/3

Akash Kumar Dutta
98 Points
8 years ago

Dear Shuvam,
The question is not in INDETERMINATE FORM.
you need to convert it in that form by using a simple formula...

:-  lim x->a   [ 1 + f(x)]^g(x)  =   e^lim x->a  f(x).g(x)

apply this formula and you get the ans as e^1/2 in the first one.

for the second put m=1/n
hence when m->infinity.... n->0
and then apply the same formula
you get the ans as 1.


Regards.

Prajwal kr
49 Points
8 years ago

Let me give you a brief idea:

It is in 1infinity form.

If f(x)=g(x)=0 when limit x tends to 0:

 

ltx tends 0f(x)g(x)=elt ((f(x)-1)g(x)

apply this formula and solve by l hospital rule. 

Gautham Pai M K
35 Points
8 years ago

as x tends to zero tanx/x tends to 1 but 1/x^2 tends to infinity.Hence, it is 1^infinity. so we use a standard result which is (1+(tanx/x)-1)^the reciprocal*1/x^2 . Hence we have the limit is e^1/3

mohit yadav
54 Points
8 years ago

e^1/3

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free