Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Solve Q22 explaining detailly each step
![16. i) Given that y+x- 2y= 0, find in terms of x and y.
dx
d'y
ii) Given that x =t'. y= 1/t, find
in terms of t.
dx2
17. Given that x =e" and y = e3, find in terms of x.
dy
dx
18. Differentiate +2ln(with respect to x and express your answer as a single
fraction
19. i) Differentiate sinx with respect to x from first principle
dy
1+3x
ii) Find,
dx
when a) y = (x sinx) b. y= In(
1-tanz
20. Find, given that
dx
1-x
a) y = arctan(), simplifying your answer as much as possible,
b) y = In(x'-3x² + 6)?
1+x
c) x=y 3t + 1, leaving your answer in terms of the parameter t.
21. i) Differentiate, with respect to x,
In(3x2)
a)
b)tan( 3x -)
ii) Given that y=e" + sin0, x = e" + cose find
dx
dy
when 0=
22. Find
when t=, where x = a(t + sint), y= a(1-cost) and a is a constant
23.If y e'lnx, show that+(1 - 2y +(x-1)y 0
24. Given x -y = 14 y, show that (1- 2y) -2(1+()
=D2
25. Differentiate cos0 with respect to 0 from the first principles.(
26. i) differentiate, with respect to x
a) cos (2Vx)
In(2x)
b)
27. Differentiate y with respeet to x where y=cos(-3x)
28. (i) Find
where
a) y = In
b) x+ y+ cosxy = 0
dy
(ii) Given that x = e'cost and y e'sint, find
wh
dx
54](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a6d9c67-6f13-49d2-ac4d-2d996f90a88b%2Fab5283ac-1fde-4442-96da-2d20e13129bb%2Fxsjxm8r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:16. i) Given that y+x- 2y= 0, find in terms of x and y.
dx
d'y
ii) Given that x =t'. y= 1/t, find
in terms of t.
dx2
17. Given that x =e" and y = e3, find in terms of x.
dy
dx
18. Differentiate +2ln(with respect to x and express your answer as a single
fraction
19. i) Differentiate sinx with respect to x from first principle
dy
1+3x
ii) Find,
dx
when a) y = (x sinx) b. y= In(
1-tanz
20. Find, given that
dx
1-x
a) y = arctan(), simplifying your answer as much as possible,
b) y = In(x'-3x² + 6)?
1+x
c) x=y 3t + 1, leaving your answer in terms of the parameter t.
21. i) Differentiate, with respect to x,
In(3x2)
a)
b)tan( 3x -)
ii) Given that y=e" + sin0, x = e" + cose find
dx
dy
when 0=
22. Find
when t=, where x = a(t + sint), y= a(1-cost) and a is a constant
23.If y e'lnx, show that+(1 - 2y +(x-1)y 0
24. Given x -y = 14 y, show that (1- 2y) -2(1+()
=D2
25. Differentiate cos0 with respect to 0 from the first principles.(
26. i) differentiate, with respect to x
a) cos (2Vx)
In(2x)
b)
27. Differentiate y with respeet to x where y=cos(-3x)
28. (i) Find
where
a) y = In
b) x+ y+ cosxy = 0
dy
(ii) Given that x = e'cost and y e'sint, find
wh
dx
54
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