Explanation Given: y = x 2 − 1 x 2 + 1 Concept Used: To find an equation of the tangent line to the graph of an equation y = f ( x ) at the a point ( a , b ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) Now, the equation of the tangent line to the graph of the equation is y = m x + c Put ( a , b ) coordinate in y = m x + c to find the value of c Calculation: To find an equation of the tangent line to the curve y = x 2 − 1 x 2 + 1 at ( 0 , − 1 ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) For that differentiate both side of the equation with respect to x as d d x y = d d x ( x 2 − 1 x 2 + 1 ) d y d x = ( x 2 − 1 ) d d x ( 1 x 2 + 1 ) + 1 x 2 + 1 d d x ( x 2 − 1 ) d y d x = ( x 2 − 1 ) d d x ( x 2 + 1 ) − 1 + 1 x 2 + 1 ( 2 x ) <

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Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3, Problem 56E

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To find an equation of the tangent line to the curve y=x2−1x2+1 at (0,−1)

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Chapter 3, Problem 55E

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8:38 *** TEMU TEMU -3 -2 7 B 2 1 & 5G. 61% 1 2 -1 Based on the graph above, determine the amplitude, period, midline, and equation of the function. Use f(x) as the output. Amplitude: 2 Period: 2 Midline: 2 ☑ syntax error: this is not an equation. Function: f(x) = −2 cos(πx + 2.5π) +2× Question Help: Worked Example 1 ☑ Message instructor Submit Question ||| <

8:39 *** TEMU 5G 60% A ferris wheel is 28 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the amplitude? 14 meters What is the equation of the Midline? y = 16 What is the period? 4 meters minutes The equation that models the height of the ferris wheel after t minutes is: f(t): = ƒ (3) = ·−14(0) + 16 syntax error: you gave an equation, not an expression. syntax error. Check your variables - you might be using an incorrect one. How high are you off of the ground after 3 minutes? Round your answe the nearest meter. ||| <

Chapter 3 Solutions

Biocalculus

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To find an equation of the tangent line to the curve y = x 2 − 1 x 2 + 1 at ( 0 , − 1 )

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To find an equation of the tangent line to the curve y=x2−1x2+1 at (0,−1)

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