Explanation Given: o lim x → ∞ tan − 1 x By definition, the inverse tangent function allows us to find the measure of an angle in a right triangle. As its name implies, it is the inverse of the tangent function. While tangent will find the ratio of the two sides of a right triangle when given an angle, inverse tangent can find the angle given the ratio. Thus, to determine lim x → ∞ tan − 1 x let us first identify geometrically what x → ∞ means in a right triangle. A right triangle is a triangle in which one angle is a right angle. The side opposite the right angle is called the hypotenuse. It is the largest side of a right-angled triangle. Assuming that one of the other two angles is θ , the side opposite to θ is called the opposite and the remaining side next to θ is called the adjacent. In a right triangle the tangent function is given by the ratio of the sides – opposite and adjacent. The following figure illustrates this nomenclature. Tan θ = Opposite Adjacent ⇒ Tan − 1 ( Opposite Adjacent ) = θ The tangent of the angle θ is the ratio of the sides opposite and adjacent. Thus, the inverse function is the function that allows us to find the measure of an angle from the ratio of the sides opposite and adjacent. By substituting x = Opposite Adjacent in the given limit we can explain it geometrically. Calculations: Description lim x → ∞ tan − 1 x Step 1: Substitute x = Opposite Adjacent in the given limit lim x → ∞ tan − 1 x lim x → ∞

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ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 2.7, Problem 35E

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The given limit using geometric explanation

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Chapter 2.7, Problem 34E

Chapter 2.7, Problem 36E

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The given limit using geometric explanation

Solution Summary: The author explains that the inverse tangent function allows us to find the measure of an angle in a right triangle.

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