Question

lim x tends to zero ( 1+2x)^1/x = e^2​

Answer 1

Step-by-step explanation:

y=(1+2x)^1/x

logy=1/x log(1+2x)

limit on b/s ,we get

lim x tends to 0 log(1+2x)/x

multiply and divide by 2

lim x tends to zero log(1+2x)×2/ 2x

w.k.t lim x tends to zero log(1+y)/y=1

2×lim x tends to zero log(1+2x)/2x=2×1=2

lim x tends to zero log(1+2x)×1/x=2

take exponential on b/s

lim x tends to zero (1+2x)^1/x=e^2