Let it be known thatx→1limf(x)=+∞,x→1limg(x)=−∞,x→1limv(x)=0, Find the values of the following limits:3) limx→1(g(x)+v(x));4) limx→1g(x)1;5) limx→1f(x)v(x);
Q. Let it be known thatx→1limf(x)=+∞,x→1limg(x)=−∞,x→1limv(x)=0, Find the values of the following limits:3) limx→1(g(x)+v(x));4) limx→1g(x)1;5) limx→1f(x)v(x);
Limit Sum Property:limx→1(g(x)+v(x)) is the sum of the limits of g(x) and v(x) as x approaches 1.limx→1g(x)=−∞ and limx→1v(x)=0.So, limx→1(g(x)+v(x))=−∞+0=−∞.
Reciprocal Limit Property:limx→1g(x)1 is the reciprocal of the limit of g(x) as x approaches 1.\lim_{x \rightarrow 1}g(x) = -\infty\.So, limx→1g(x)1=−∞1=0.
Ratio Limit Property:limx→1f(x)v(x) is the ratio of the limits of v(x) and f(x) as x approaches 1.limx→1v(x)=0 and limx→1f(x)=+∞.So, limx→1f(x)v(x)=+∞0=0.