If limit (1 + ax)b/x = e4 where a and b are natural numbers then values of a and b - Maths - Limits and Derivatives

Question

If limit (1 + ax)b/x = e4 where a and b are
natural numbers then values of a and b = ?

Ajanta Trivedi · Accepted Answer

if limx→a f(x)=limx→ag(x)=0 such that f(x)g(x) existsthen limx→a1+f(x)1/g(x)=elimx→af(x)g(x)
if the given limit is
limx→01+axb/x=elimx→0ax*bx=elimx→0ab=eabcomparing from the given equation , we haveab=4⇒a=2 and b=2 or a =1 and b=4 [since a and b are natural numbers

hope this helps you

If limit (1 + ax)b/x = e4 where a and b are natural numbers then values of a and b = ?

If limit (1 + ax)^b/x = e⁴ where a and b are natural numbers then values of a and b = ?