Let g(x)=tan2(x)1.Select the correct description of the one-sided limits of g at x=0.Choose 1 answer:(A)limx→0+g(x)=+∞ and limx→0−g(x)=+∞(B)limx→0+g(x)=+∞ and limx→0−g(x)=−∞(C)limx→0+g(x)=−∞ and limx→0−g(x)=+∞(D)limx→0+g(x)=−∞ and limx→0−g(x)=−∞
Q. Let g(x)=tan2(x)1.Select the correct description of the one-sided limits of g at x=0.Choose 1 answer:(A)limx→0+g(x)=+∞ and limx→0−g(x)=+∞(B)limx→0+g(x)=+∞ and limx→0−g(x)=−∞(C)limx→0+g(x)=−∞ and limx→0−g(x)=+∞(D)limx→0+g(x)=−∞ and limx→0−g(x)=−∞
Behavior of Tangent Function: Understand the behavior of the tangent function near zero.The tangent function, tan(x), approaches 0 as x approaches 0 from both the positive and negative sides. Since g(x)=tan2(x)1, we need to consider what happens when we take the reciprocal of a number that is approaching zero.
Limit as x Approaches 0 from Positive Side: Consider the limit of g(x) as x approaches 0 from the positive side.As x approaches 0 from the positive side, tan(x) approaches 0, and thus tan2(x) also approaches 0. Taking the reciprocal of a positive number that is getting closer and closer to zero will result in a number that grows without bound. Therefore, the limit of g(x) as x approaches 0 from the positive side is positive infinity.04
Limit as x Approaches 0 from Negative Side: Consider the limit of g(x) as x approaches 0 from the negative side.As x approaches 0 from the negative side, tan(x) approaches 0, and thus tan2(x) also approaches 0. Taking the reciprocal of a positive number that is getting closer and closer to zero will result in a number that grows without bound. Since tan2(x) is positive whether x approaches from the left or right, the limit from the negative side is also positive infinity.03
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