42. g(x) = 2x sinx sec x %3D In Exercises 43-46, find the equations of the tangent lin the graph of g at the indicated point. 43. g(s) = e (s? + 2) at (0, 2). 44. g(t) = t sin t at (,-)
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.
Hi I need help answering 42, 44, and 49. Please show work thank you.
![39. F(x) = (8x – 1)(x² + 4x + 7)(x³ – 5)
t? sin t + 3
13. f(x) — (x + 5)(3 — х)
40. h(t)
t2 cos t + 2
In Exercises 14-17:
41. f(x) = x'e* tan x
(a) Use the Quotient Rule to differentiate the function.
42. g(x) = 2x sin x sec x
(b) Manipulate the function algebraically and differentiate
without the Quotient Rule.
In Exercises 43–46, find the equations of the tangent line to
the graph of g at the indicated point.
(c) Show that the answers from (a) and (b) are equivalent.
x2 + 3
43. g(s) — е' (s+ 2) at (0, 2).
44. g(t) = t sin t at (, -)
14. f(x) =
x – 2x?
15. g(x)
x²
at (2, 4)
2x2
45. g(x)
X - 1
3
16. h(s) =
453
cos 0
46. g(0) =
0 +1
80
at (0, 1)
t2 - 1
17. f(t) =
t+1
In Exercises 47–50, find the x-values where the graph of the
function has a horizontal tangent line.
In Exercises 18-42, compute the derivative of the given func-
tion.
47. f(x) = 6x – 18x – 24
119
48. f(x) = x sin x on [–1, 1]
g
(2)
60.
49. f(x)
x + 1
61. If f and g are functions whose graphs are shown, evaluate
the expressions.
x²
50. f(x)
X +1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf266520-407e-4b51-839c-e1d92d759be6%2F272c5dbd-0f79-4d1b-8e9a-158afa230395%2Fvn761dqi_processed.jpeg&w=3840&q=75)
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