Question

Lim x tends to infinity x^2+5x-2/2x^2+5x+1​

Answer 1

Answer:

limx→∞(x2+5x+3x2+x+2)x

limx→∞(x2+x+2+4x+1x2+x+2)x

limx→∞(1+4x+1x2+x+2)x

limx→∞(1+4x+1x2+x+2)x2+x+24x+1⋅4x+1x2+x+2⋅x

limx→∞(1+1f(x))f(x)⋅g(x)

f(x)=x2+x+24x+1 and g(x)=(4x+1)⋅xx2+x+2

also we know that

limf(x)→∞(1+1f(x))f(x)=e

so answer will be

elimx→∞g(x)

because limx→∞f(x)=limx→∞x2+x+24x+1=∞

limx→∞g(x)=limx→∞(4x+1)⋅xx2+x+2=4

limx→∞(x2+5x+3x2+x+2)x=elimx→∞g(x)=e4