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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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.
Question
Solve all Q36 explaining detailly each step
![II. b) Application:
28. Find the area of the finite region in the first quadrant bounded by the curves y = e°, y=e*,
x = In2.
d²y
dy
+ 13y = 0
3x
29. a) Given that y = e*sin2x, show that:
dx²
dx
%3D
b) Solve the differential equation (x- 4)-- + 2xy = 0, (x ±2). given that y = 1/5 when x =
dx
3.
30. i) Find in the form y = f(x), the general solution of the differential equation:
dy
x²-1
(1+x*)–-2x(1-y)= 0. Given that y = 0 when x = 1, show that f(x)
31. Find the area of the finite region bounded by the curves y = x(10 - x) and y = x (3x+ 2).
|
dx
x²+1
dy
32. Show that the solution of the differential equation (x + x – 2)-
+ 2x + 1 =0 for which y=
di
1
- and x= 2 is y= Sketch the integral curve corresponding to this solution showing
4
(x+1)(x+2)
clearly all the vertical and horizontal asymptotes and turning points.
áy
33. Solve in the form y = f(x), the differential equation: x
= v (2x + 1). Hence on a separate
diagram, skeich aiso the graph of y = f(x)|.
34. Find the area of the finite region enclosed by the curve xy = 1 and line x+y = 4, leaving
your answer in terms of naturai logarithms.
35. Find the total area of the finite regions bounded by the crve y = x(2- X), the x-axis and the
ordinate at x =
3D3.
36. Solve the differential equation (x-2)(x+3)-- (2x+1)= 0 given that y= In6 when x =
dy
36
37. Find the general solution of the differential equation: x = Inx + y Inx, expressing your
dy
dx
answer in the form y = f(x).
38. The table given values of a continuous variable y corresponding to the given values of x.
1
3
7
27
65
119
a. Use the trapezium rule to find an estimate for vdx.
b. A relation of the form y = ax´+bx is known to exist between x and y. By plotting-against
X. estimate the values of the constant a and b to the nearest interger. Hence, obtain another
7
estimate for f ydx by direct intergration.(
39. Find the area of the region enclosed by the curve with equation: y = x(2 – x) and theline
y = x.
60
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a6d9c67-6f13-49d2-ac4d-2d996f90a88b%2F2c8751ab-01c8-4572-aea0-3e93e6050c7b%2Fmuuarp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:II. b) Application:
28. Find the area of the finite region in the first quadrant bounded by the curves y = e°, y=e*,
x = In2.
d²y
dy
+ 13y = 0
3x
29. a) Given that y = e*sin2x, show that:
dx²
dx
%3D
b) Solve the differential equation (x- 4)-- + 2xy = 0, (x ±2). given that y = 1/5 when x =
dx
3.
30. i) Find in the form y = f(x), the general solution of the differential equation:
dy
x²-1
(1+x*)–-2x(1-y)= 0. Given that y = 0 when x = 1, show that f(x)
31. Find the area of the finite region bounded by the curves y = x(10 - x) and y = x (3x+ 2).
|
dx
x²+1
dy
32. Show that the solution of the differential equation (x + x – 2)-
+ 2x + 1 =0 for which y=
di
1
- and x= 2 is y= Sketch the integral curve corresponding to this solution showing
4
(x+1)(x+2)
clearly all the vertical and horizontal asymptotes and turning points.
áy
33. Solve in the form y = f(x), the differential equation: x
= v (2x + 1). Hence on a separate
diagram, skeich aiso the graph of y = f(x)|.
34. Find the area of the finite region enclosed by the curve xy = 1 and line x+y = 4, leaving
your answer in terms of naturai logarithms.
35. Find the total area of the finite regions bounded by the crve y = x(2- X), the x-axis and the
ordinate at x =
3D3.
36. Solve the differential equation (x-2)(x+3)-- (2x+1)= 0 given that y= In6 when x =
dy
36
37. Find the general solution of the differential equation: x = Inx + y Inx, expressing your
dy
dx
answer in the form y = f(x).
38. The table given values of a continuous variable y corresponding to the given values of x.
1
3
7
27
65
119
a. Use the trapezium rule to find an estimate for vdx.
b. A relation of the form y = ax´+bx is known to exist between x and y. By plotting-against
X. estimate the values of the constant a and b to the nearest interger. Hence, obtain another
7
estimate for f ydx by direct intergration.(
39. Find the area of the region enclosed by the curve with equation: y = x(2 – x) and theline
y = x.
60
2.
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