7-8 Find an equation of the tangent to the curve at the given noint by two methods: (a) without eliminating the parameter and (b) by first eliminating the parameter. be 7. x 1 + In t, y t2 + 2; (1, 3) 8. x= 1 + Vt, y= e"; (2, e) y = e"; (2, e) %3D 9-10 Find an equation of the tangent to the curve at the given point. Then graph the curve and the tangent. to 9. x = t-t, y=t +t + 1; (0, 3) elq 10. x = sin Tt, y=t2 + t; (0,2) 11-16 Find dy/dx and d?y/dx?. For which values of t is the curve concave upward? 3 11. x = t2 + 1, y=t + t 12. x = t + 1, y=t - t 13. x = e', y = te 14. x = t2 + 1, y e'- 1 1- 15. x = t - In t, oy t+ In t is 16. x = cos t, y = sin 2t, 0

Calculus: Early Transcendentals
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Chapter1: Functions And Models
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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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7-8 Find an equation of the tangent to the curve at the given
noint by two methods: (a) without eliminating the parameter and
(b) by first eliminating the parameter.
be
7. x 1 + In t, y t2 + 2; (1, 3)
8. x= 1 + Vt, y= e"; (2, e)
y = e"; (2, e)
%3D
9-10 Find an equation of the tangent to the curve at the given
point. Then graph the curve and the tangent.
to
9. x = t-t, y=t +t + 1; (0, 3)
elq
10. x = sin Tt, y=t2 + t; (0,2)
11-16 Find dy/dx and d?y/dx?. For which values of t is the
curve concave upward?
3
11. x = t2 + 1, y=t + t
12. x = t + 1, y=t - t
13. x = e', y = te
14. x = t2 + 1, y e'- 1
1-
15. x = t - In t, oy t+ In t
is
16. x = cos t,
y = sin 2t, 0<t<T
17-20 Find the points on the curve where the tangent is hori-
zontal or vertical. If you have a graphing device, graph the curve
to check your work.
17. x = t3 - 3t, y t2- 3
18. x = t- 3t, y= t- 3t2
19. x = cos 0, y= cos 30
20. x = eo,
y3D e cos 0
estimate the coordinates of the rightmost
rve r=
76
Ee Then use calculus to
Transcribed Image Text:7-8 Find an equation of the tangent to the curve at the given noint by two methods: (a) without eliminating the parameter and (b) by first eliminating the parameter. be 7. x 1 + In t, y t2 + 2; (1, 3) 8. x= 1 + Vt, y= e"; (2, e) y = e"; (2, e) %3D 9-10 Find an equation of the tangent to the curve at the given point. Then graph the curve and the tangent. to 9. x = t-t, y=t +t + 1; (0, 3) elq 10. x = sin Tt, y=t2 + t; (0,2) 11-16 Find dy/dx and d?y/dx?. For which values of t is the curve concave upward? 3 11. x = t2 + 1, y=t + t 12. x = t + 1, y=t - t 13. x = e', y = te 14. x = t2 + 1, y e'- 1 1- 15. x = t - In t, oy t+ In t is 16. x = cos t, y = sin 2t, 0<t<T 17-20 Find the points on the curve where the tangent is hori- zontal or vertical. If you have a graphing device, graph the curve to check your work. 17. x = t3 - 3t, y t2- 3 18. x = t- 3t, y= t- 3t2 19. x = cos 0, y= cos 30 20. x = eo, y3D e cos 0 estimate the coordinates of the rightmost rve r= 76 Ee Then use calculus to
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