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Let 
h(x)=-(5)/(x).
Select the correct description of the one-sided limits of 
h at 
x=0.
Choose 1 answer:
(A) 
lim_(x rarr0^(+))h(x)=+oo and 
lim_(x rarr0^(-))h(x)=+oo
(B) 
lim_(x rarr0^(+))h(x)=+oo and 
lim_(x rarr0^(-))h(x)=-oo
(C) 
lim_(x rarr0^(+))h(x)=-oo and 
lim_(x rarr0^(-))h(x)=+oo
(D) 
lim_(x rarr0^(+))h(x)=-oo and 
lim_(x rarr0^(-))h(x)=-oo

Let h(x)=5x h(x)=-\frac{5}{x} .\newlineSelect the correct description of the one-sided limits of h h at x=0 x=0 .\newlineChoose 11 answer:\newline(A) limx0+h(x)=+ \lim _{x \rightarrow 0^{+}} h(x)=+\infty and limx0h(x)=+ \lim _{x \rightarrow 0^{-}} h(x)=+\infty \newline(B) limx0+h(x)=+ \lim _{x \rightarrow 0^{+}} h(x)=+\infty and limx0h(x)= \lim _{x \rightarrow 0^{-}} h(x)=-\infty \newline(C) limx0+h(x)= \lim _{x \rightarrow 0^{+}} h(x)=-\infty and limx0h(x)=+ \lim _{x \rightarrow 0^{-}} h(x)=+\infty \newline(D) limx0+h(x)= \lim _{x \rightarrow 0^{+}} h(x)=-\infty and limx0h(x)= \lim _{x \rightarrow 0^{-}} h(x)=-\infty

Full solution

Q. Let h(x)=5x h(x)=-\frac{5}{x} .\newlineSelect the correct description of the one-sided limits of h h at x=0 x=0 .\newlineChoose 11 answer:\newline(A) limx0+h(x)=+ \lim _{x \rightarrow 0^{+}} h(x)=+\infty and limx0h(x)=+ \lim _{x \rightarrow 0^{-}} h(x)=+\infty \newline(B) limx0+h(x)=+ \lim _{x \rightarrow 0^{+}} h(x)=+\infty and limx0h(x)= \lim _{x \rightarrow 0^{-}} h(x)=-\infty \newline(C) limx0+h(x)= \lim _{x \rightarrow 0^{+}} h(x)=-\infty and limx0h(x)=+ \lim _{x \rightarrow 0^{-}} h(x)=+\infty \newline(D) limx0+h(x)= \lim _{x \rightarrow 0^{+}} h(x)=-\infty and limx0h(x)= \lim _{x \rightarrow 0^{-}} h(x)=-\infty
  1. Approaching 00 from the positive side: Consider the function h(x)=5xh(x) = -\frac{5}{x} and what happens as xx approaches 00 from the positive side (right-hand limit). As xx gets closer to 00 from the positive side, the value of 1x\frac{1}{x} becomes very large, and since we have a negative sign in front of the 55, h(x)h(x) will approach negative infinity.
  2. Calculating the right-hand limit: Calculate the right-hand limit of h(x)h(x) as xx approaches 00.limx0+h(x)=limx0+5x=\lim_{x \rightarrow 0^{+}}h(x) = \lim_{x \rightarrow 0^{+}}-\frac{5}{x} = -\infty
  3. Approaching 00 from the negative side: Consider the function h(x)=5xh(x) = -\frac{5}{x} and what happens as xx approaches 00 from the negative side (left-hand limit). As xx gets closer to 00 from the negative side, the value of 1x\frac{1}{x} becomes very large in the negative direction, and since we have a negative sign in front of the 55, h(x)h(x) will approach positive infinity.
  4. Calculating the left-hand limit: Calculate the left-hand limit of h(x)h(x) as xx approaches 00.limx0h(x)=limx05x=+\lim_{x \to 0^{-}}h(x) = \lim_{x \to 0^{-}}-\frac{5}{x} = +\infty

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