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etry. We are also implicitly solving a great in science and engineering. 2.1 EXERCISES 1. A curve has equation y =f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P. (b) F at (c) C in 2. Graph the curve y = sin x in the viewing rectangles 11. (a) [-2, 2] by [-2, 2], [-1, 1] by [-1, 1], and [-0.5, 0.5] by [-0.5, 0.5]. What do you notice about the curve as you zoom in toward the origin? 3. (a) Find the slope of the tangent line to the parabola y = 4x - x² at the point (1, 3) (b) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (1, 3) until the parabola and the tangent line are indistinguishable. (ii) using Equation 2 4. (a) Find the slope of the tangent line to the curve y = x – x' at the point (1, 0) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the curve and the tangent line in successively smaller viewing rectangles centered at (1, 0) until the curve and the line appear to coincide. (ii) using Equation 2 12. 5-8 Find an equation of the tangent line to the curve at the given point. 6. y = x³ – 3x + 1, (2, 3) 3x², (2, -4) 5. y = 4x – 2x + 1 (1, 1) 7. y= Vx, (1, 1) 8. y = x+ 2 (0) 1 Definition The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope f(x) - f(a) m = lim provided that this limit exists.

etry. We are also implicitly solving a great in science and engineering. 2.1 EXERCISES 1. A curve has equation y =f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P. (b) F at (c) C in 2. Graph the curve y = sin x in the viewing rectangles 11. (a) [-2, 2] by [-2, 2], [-1, 1] by [-1, 1], and [-0.5, 0.5] by [-0.5, 0.5]. What do you notice about the curve as you zoom in toward the origin? 3. (a) Find the slope of the tangent line to the parabola y = 4x - x² at the point (1, 3) (b) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (1, 3) until the parabola and the tangent line are indistinguishable. (ii) using Equation 2 4. (a) Find the slope of the tangent line to the curve y = x – x' at the point (1, 0) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the curve and the tangent line in successively smaller viewing rectangles centered at (1, 0) until the curve and the line appear to coincide. (ii) using Equation 2 12. 5-8 Find an equation of the tangent line to the curve at the given point. 6. y = x³ – 3x + 1, (2, 3) 3x², (2, -4) 5. y = 4x – 2x + 1 (1, 1) 7. y= Vx, (1, 1) 8. y = x+ 2 (0) 1 Definition The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope f(x) - f(a) m = lim provided that this limit exists.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Equation 2:      m= lim (f(a +h)- f(a))/(h)

                            h➡️0 

etry. We are also implicitly solving a great in science and engineering. 2.1 EXERCISES 1. A curve has equation y =f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P. (b) F at (c) C in 2. Graph the curve y = sin x in the viewing rectangles 11. (a) [-2, 2] by [-2, 2], [-1, 1] by [-1, 1], and [-0.5, 0.5] by [-0.5, 0.5]. What do you notice about the curve as you zoom in toward the origin? 3. (a) Find the slope of the tangent line to the parabola y = 4x - x² at the point (1, 3) (b) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (1, 3) until the parabola and the tangent line are indistinguishable. (ii) using Equation 2 4. (a) Find the slope of the tangent line to the curve y = x – x' at the point (1, 0) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the curve and the tangent line in successively smaller viewing rectangles centered at (1, 0) until the curve and the line appear to coincide. (ii) using Equation 2 12. 5-8 Find an equation of the tangent line to the curve at the given point. 6. y = x³ – 3x + 1, (2, 3) 3x², (2, -4) 5. y = 4x – 2x + 1 (1, 1) 7. y= Vx, (1, 1) 8. y = x+ 2 (0)
Transcribed Image Text:etry. We are also implicitly solving a great in science and engineering. 2.1 EXERCISES 1. A curve has equation y =f(x). (a) Write an expression for the slope of the secant line through the points P(3, f(3)) and Q(x, f(x)). (b) Write an expression for the slope of the tangent line at P. (b) F at (c) C in 2. Graph the curve y = sin x in the viewing rectangles 11. (a) [-2, 2] by [-2, 2], [-1, 1] by [-1, 1], and [-0.5, 0.5] by [-0.5, 0.5]. What do you notice about the curve as you zoom in toward the origin? 3. (a) Find the slope of the tangent line to the parabola y = 4x - x² at the point (1, 3) (b) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (1, 3) until the parabola and the tangent line are indistinguishable. (ii) using Equation 2 4. (a) Find the slope of the tangent line to the curve y = x – x' at the point (1, 0) (i) using Definition 1 (b) Find an equation of the tangent line in part (a). (c) Graph the curve and the tangent line in successively smaller viewing rectangles centered at (1, 0) until the curve and the line appear to coincide. (ii) using Equation 2 12. 5-8 Find an equation of the tangent line to the curve at the given point. 6. y = x³ – 3x + 1, (2, 3) 3x², (2, -4) 5. y = 4x – 2x + 1 (1, 1) 7. y= Vx, (1, 1) 8. y = x+ 2 (0)
1 Definition The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope f(x) - f(a) m = lim provided that this limit exists.
Transcribed Image Text:1 Definition The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope f(x) - f(a) m = lim provided that this limit exists.
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