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Instructions: In problems 1-15, use the derivative rules to find the derivative of y in each case. 1. y = (2x-7)³ 2. y = (3x² +1)* 3. y=3x (4-9x)* 4. y=(3 + x)² (1 − x²)³ 5. y=(9-x²) ²/3 7. y = √√9x² + 2x + 7 10. y= x + 1 x-1 13. y=(x+¹)* 1 (ii) 8. y= lim to+ 11. y 17. Bonus Set M=(1,0), N= (0, 1), O = (0,0), and P,= (t,√t) for t> 0. Compute: (i) Area(AMOP) lim t-0+ Area(ANOP) - 2x + 1 Perimeter (AMOP) Perimeter (ANOP,) 6x - 5 2 x + 1 6. y=√√3-2x 2x³ 1 M 9. y 12. (4x-1)³ 14. y = x²(x −1)² 2x² +1 16. Bonus Use calculus to find the coordinates of the two points along the graph of y=4-x² whose tangent lines pass through point P = (1,7). Then sketch a graph which displays the parabola and both of its tangent lines which intersect at P. Also, determine the angles of inclinations of these tangent lines. (Recall, m = tan a, if a is the inclination of the line with slope m.) Hint: Describe the parabola parametrically to find the two points - refer to problem 4 of Worksheet 5. y=√x y = 15. y = X 3x 2 2x + 3 2 - 2x

Instructions: In problems 1-15, use the derivative rules to find the derivative of y in each case. 1. y = (2x-7)³ 2. y = (3x² +1)* 3. y=3x (4-9x)* 4. y=(3 + x)² (1 − x²)³ 5. y=(9-x²) ²/3 7. y = √√9x² + 2x + 7 10. y= x + 1 x-1 13. y=(x+¹)* 1 (ii) 8. y= lim to+ 11. y 17. Bonus Set M=(1,0), N= (0, 1), O = (0,0), and P,= (t,√t) for t> 0. Compute: (i) Area(AMOP) lim t-0+ Area(ANOP) - 2x + 1 Perimeter (AMOP) Perimeter (ANOP,) 6x - 5 2 x + 1 6. y=√√3-2x 2x³ 1 M 9. y 12. (4x-1)³ 14. y = x²(x −1)² 2x² +1 16. Bonus Use calculus to find the coordinates of the two points along the graph of y=4-x² whose tangent lines pass through point P = (1,7). Then sketch a graph which displays the parabola and both of its tangent lines which intersect at P. Also, determine the angles of inclinations of these tangent lines. (Recall, m = tan a, if a is the inclination of the line with slope m.) Hint: Describe the parabola parametrically to find the two points - refer to problem 4 of Worksheet 5. y=√x y = 15. y = X 3x 2 2x + 3 2 - 2x

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Instructions: In problems 1-15, use the derivative rules to find the derivative of y in each case. 1. y = (2x-7)³ 2. y = (3x² +1)* 3. y=3x (4-9x)* 4. y=(3 + x)² (1 − x²)³ 5. y=(9-x²) ²/3 7. y = √√9x² + 2x + 7 10. y= x + 1 x-1 13. y=(x+¹)* 1 (ii) 8. y= lim to+ 11. y 17. Bonus Set M=(1,0), N= (0, 1), O = (0,0), and P,= (t,√t) for t> 0. Compute: (i) Area(AMOP) lim t-0+ Area(ANOP) - 2x + 1 Perimeter (AMOP) Perimeter (ANOP,) 6x - 5 2 x + 1 6. y=√√3-2x 2x³ 1 M 9. y 12. (4x-1)³ 14. y = x²(x −1)² 2x² +1 16. Bonus Use calculus to find the coordinates of the two points along the graph of y=4-x² whose tangent lines pass through point P = (1,7). Then sketch a graph which displays the parabola and both of its tangent lines which intersect at P. Also, determine the angles of inclinations of these tangent lines. (Recall, m = tan a, if a is the inclination of the line with slope m.) Hint: Describe the parabola parametrically to find the two points - refer to problem 4 of Worksheet 5. y=√x y = 15. y = X 3x 2 2x + 3 2 - 2x
Transcribed Image Text:Instructions: In problems 1-15, use the derivative rules to find the derivative of y in each case. 1. y = (2x-7)³ 2. y = (3x² +1)* 3. y=3x (4-9x)* 4. y=(3 + x)² (1 − x²)³ 5. y=(9-x²) ²/3 7. y = √√9x² + 2x + 7 10. y= x + 1 x-1 13. y=(x+¹)* 1 (ii) 8. y= lim to+ 11. y 17. Bonus Set M=(1,0), N= (0, 1), O = (0,0), and P,= (t,√t) for t> 0. Compute: (i) Area(AMOP) lim t-0+ Area(ANOP) - 2x + 1 Perimeter (AMOP) Perimeter (ANOP,) 6x - 5 2 x + 1 6. y=√√3-2x 2x³ 1 M 9. y 12. (4x-1)³ 14. y = x²(x −1)² 2x² +1 16. Bonus Use calculus to find the coordinates of the two points along the graph of y=4-x² whose tangent lines pass through point P = (1,7). Then sketch a graph which displays the parabola and both of its tangent lines which intersect at P. Also, determine the angles of inclinations of these tangent lines. (Recall, m = tan a, if a is the inclination of the line with slope m.) Hint: Describe the parabola parametrically to find the two points - refer to problem 4 of Worksheet 5. y=√x y = 15. y = X 3x 2 2x + 3 2 - 2x
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