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

Please find the limit of the question lim x->0 (((e^x+(e^-x)-2)/x^2)^(1/x^2))

Please find the limit of the question
lim x->0 (((e^x+(e^-x)-2)/x^2)^(1/x^2))

Grade:12

1 Answers

Samyak Jain
333 Points
2 years ago
 lim  { (ex + e–x – 2)/x2 }^(1/x2). It is of 1\infty.
x\rightarrow0
So, its solution is  e^(lim {(ex + e–x – 2)/x2  – 1}.(1/x2))  =  e^(lim {(ex + e–x – 2 – x2) / x2}.(1/x2))
                              x\rightarrow0
         =  e^(lim { (ex + e–x – 2 – x2) / x4 })
                x\rightarrow0
Use expansion of ex here, i.e.,
ex = 1 + x + x2/2! + x3/3! + x4/4! + …   and   e–x = 1 – x + x2/2! – x3/3! + x4/4! + …
Subtitute in the limit.
e^(lim { (ex + e–x – 2 – x2) / x4 }) =
   x\rightarrow0
e^(lim { (1 + x + x2/2! + x3/3! + x4/4! + … + 1 – x + x2/2! – x3/3! + x4/4! + … – 2 – x2) / x4 })
   x\rightarrow0
 =  e^(lim { (2.x4/4! + ...) / x4
        x\rightarrow0
 =  e^(1/12).  As x tends to zero higher powers of of x will also tend to zero, so they aren’t written here.

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