Let h(x)=−x5.Select the correct description of the one-sided limits of h at x=0.Choose 1 answer:(A) limx→0+h(x)=+∞ and limx→0−h(x)=+∞(B) limx→0+h(x)=+∞ and limx→0−h(x)=−∞(C) limx→0+h(x)=−∞ and limx→0−h(x)=+∞(D) limx→0+h(x)=−∞ and limx→0−h(x)=−∞
Q. Let h(x)=−x5.Select the correct description of the one-sided limits of h at x=0.Choose 1 answer:(A) limx→0+h(x)=+∞ and limx→0−h(x)=+∞(B) limx→0+h(x)=+∞ and limx→0−h(x)=−∞(C) limx→0+h(x)=−∞ and limx→0−h(x)=+∞(D) limx→0+h(x)=−∞ and limx→0−h(x)=−∞
Approaching 0 from the positive side: Consider the function h(x)=−x5 and what happens as x approaches 0 from the positive side (right-hand limit). As x gets closer to 0 from the positive side, the value of x1 becomes very large, and since we have a negative sign in front of the 5, h(x) will approach negative infinity.
Calculating the right-hand limit: Calculate the right-hand limit of h(x) as x approaches 0.limx→0+h(x)=limx→0+−x5=−∞
Approaching 0 from the negative side: Consider the function h(x)=−x5 and what happens as x approaches 0 from the negative side (left-hand limit). As x gets closer to 0 from the negative side, the value of x1 becomes very large in the negative direction, and since we have a negative sign in front of the 5, h(x) will approach positive infinity.
Calculating the left-hand limit: Calculate the left-hand limit of h(x) as x approaches 0.x→0−limh(x)=x→0−lim−x5=+∞