Find Horizontal Asymptote We know that if f(x) is a function and if the line ax + by + c = 0 meets the curve only at infinity, then the line ax + by + c = 0 is called an asymptote. Horizontal asymptote: It is an asymptote which is horizontal. The asymptote is thus parallel to x axis, so is of the form y = a, for all real values of a. Thus if f(x) = y is a function, then y =a, becomes undefined for the function, then the line y = a, is called the asymptote for the function y = f(x). To find out horizontal asymptote, we can visualise the curve and get when y=a, for any a, so that the curve becomes undefined. A simple example is the equation y= . This we can write as x = . The curve becomes undefined when y=0 and therefore the line y = 0 or x axis is a horizontal asymptote for the curve x= .
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The methods of finding out horizontal asymptotes for a curve, if it is a rational function: Step 1: Find out the degree of numerator and denominator. Step 2: There are three possibilities. i. degree of numerator > degree of denominator. Then we can leave this as this type of curve has no horizontal asymptotes. Suppose numerator is more than the denominator then it may turn out to be a linear or quadratic of some function of degree n-m the difference. ii. degree of numerator =degree of denominator. Then find the fraction made by the leading coefficients and equate to y. This is the horizontal asymptote. Eg: If numerator has 3x続 and denominator has 2x as leading coefficient then y = is horizontal asymptote. iii.degree of numerator < degree of denominator: then the horizontal asymptote is x axis, or y=0. Learn More Similar Triangles Worksheet
Eg: numerator has 4x4 and denominator as x then the asymptote is y=0. So let us assume if the degree of numerator as n and degree of denominator as m. Then we have if n If n =m, then y = is the horizontal asymptote. i,e, the ratio of leading coefficients of numerator and denominator. If n >m then if n =m+1, there is a slant asymptote and no horizontal asymptotes. Horizontal asymptotes are only to the extreme right or extreme left of the graph. Normally it will not be in the middle of the curve. So while finding out horizontal asymptote or checking, this hint will help us.
Arc Length of a Circle Here we are going to learn about Arc length and formula to find the Arc Length. Arc Length is nothing but length or an arc. Arc is a curve. We can also call it as arc length of a curve. Arc length is defined as the measure of the distance along the curved line making up an arc. The arc length is longer than the straight line distance between its end points. We can consider an segment in a circle, which is an arc. Consider the below figure In the figure shown above, the arc length is the blue coloured portion indicated by s. Let be the angle made by the end points with the center of the circle. The distance from one end point of the curve or arc to the center is called as radius. If we know the radius and value we can find out the arc length using the below formula. Arc Length Practice Problems Problem 1: Evaluate the arc length of a circle of diameter and the central angle 1800.
Answer : The arc length of the circle which is the semicircular arc is Problem 2: Evaluate the arc length of a circle of radius 9 cm and the central angle 1200 Answer : The arc length of the circle is 18.84 cm Example 2: Calculate the arc length of a circle with circumference 31.42 cm and the the central angle is given by 450 . Solution : Step 1: As the circumference of the circle is given, the radius of the circle can be calculated as mentioned in the above formula table.
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