31. F(t) = e' sir %3| 32. F(t) 33. G(x) = 4C/x y* + 1 34. U(y) = 1 – e2x 35. y = cOS = COS 36. у — х?е \. 1 + e2x 37. y = cot2(sin 0) 38. у — у1 + хе 2х 39. f(t) = tan(sec(cos t)) 40. y = e™ sin 2x + sin(e2*) x²)99 41. f(t) = sin²(e sin's) 42. y = vx + x+x1 43. g(x) = (2ra* + n)" 44. y = 23** 45. y = cos v sin(tan x) 46. y = [x + (x + sin²x)°]* %3D 47-50 Find y' and y". 1 47. y = cos(sin 30) 48. y = (1 + tan x)? 49. y = V1 /1 – sec t 50. y = eet 51-54 Find an equation of the tangent line to the curve at the giv point. 51. y = 2*, (0, 1) 52. y = /1 + x³, (2,3) %3D 53. y = sin(sin x), (T, 0) 54. y = xe¯, xe¯x² (0,0) 55. (a) Find an equation of the tangent line to the curve y = 2/(1 + e¯*) at the point (0, 1). (b) Illustrate part (a) by graphing the curve and the tangent on the same screen.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
I need help with problem #49 on page 204 of the James Stewart Calculus Eighth Edition textbook.
![31. F(t) = e' sir
%3|
32. F(t)
33. G(x) = 4C/x
y* + 1
34. U(y) =
1 – e2x
35. y = cOS
= COS
36. у — х?е \.
1 + e2x
37. y = cot2(sin 0)
38. у — у1 + хе 2х
39. f(t) = tan(sec(cos t))
40. y = e™
sin 2x + sin(e2*)
x²)99
41. f(t) = sin²(e sin's)
42. y = vx +
x+x1
43. g(x) = (2ra* + n)"
44. y = 23**
45. y = cos v sin(tan x)
46. y = [x + (x + sin²x)°]*
%3D
47-50 Find y' and y".
1
47. y = cos(sin 30)
48. y =
(1 + tan x)?
49. y = V1
/1 – sec t
50. y = eet
51-54 Find an equation of the tangent line to the curve at the giv
point.
51. y = 2*, (0, 1)
52. y = /1 + x³, (2,3)
%3D
53. y = sin(sin x), (T, 0)
54. y = xe¯,
xe¯x²
(0,0)
55. (a) Find an equation of the tangent line to the curve
y = 2/(1 + e¯*) at the point (0, 1).
(b) Illustrate part (a) by graphing the curve and the tangent
on the same screen.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9b9bfc7b-5e86-435c-b9dd-a07d54ff6a7e%2F488f9919-e1a7-4b65-a8ee-ceea601b10c7%2Fqnko2c.jpeg&w=3840&q=75)
Given the function
Find y’ using chain rule.
Substitute the value of u.
We have found
Find y”
Step by step
Solved in 8 steps with 10 images
