Q ) limx--- infinity (1+ 1/(a+bx))c + dx= where (a,b,c,d 0) - Maths - Limits and Derivatives

Question

Q ) limx--- infinity (1+
1/(a+bx)​)c + dx= where
(a,b,c,d>0)
​

Devesh Kumar · Accepted Answer

limx→∞1+1a+bxc+dxLet x = 1yas x→∞, then y→0Now, limy→0 1 + 1a+byc+dy=limy→01 + yay+bcy+dy=limy→0ay+b+yay+bcy+dy=limy→0a+1y + bay+bcy+dy=limy→0ay+bay+b + yay+bcy+dy=limy→01 + yay+bay+by × yay+b × cy+dy=limy→01 + yay+bay+bycy+day+b=elimy→0cy+day+b=ed/b

Q ) limx--- infinity (1+ 1/(a+bx)​)c + dx= where (a,b,c,d>0) ​

Q ) lim_{x--- infinity} (1+ 1/(a+bx))^{c + dx}= where (a,b,c,d>0)