Question 3.55) Differentiate the following functions. Simplify your answers as much as possible. B) cos³ (csc¯¹(1²+2)) (remember to simplify...) A) [sin`¯¹(1−rª)]² C) tan (√r arccos(√r)) cot ¹(x³) csc(x³) D)
Question 3.55) Differentiate the following functions. Simplify your answers as much as possible. B) cos³ (csc¯¹(1²+2)) (remember to simplify...) A) [sin`¯¹(1−rª)]² C) tan (√r arccos(√r)) cot ¹(x³) csc(x³) D)
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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Can you please answer question 3.55
![Question 3.51)
Find the value of the following.
Make sure to show the data in the unit circle and/or in right triangles to justify your answers.
A) arcsin (2)
B) arccos (-√2)
C) arctan(-Ys)
D) arccot (cot(-3))
E) sec (arccsc()) (Use a right triangle).
Question 3.52)
Consider the curves y=f(x)=x² and y=g(x)=(x−2)² - 2.
Find the acute angle of intersection between the curves.
Procedure:-Find the point of intersection.
- Find the slope of both tangents lines at that point.
- Use an inverse trigonometric f" (show this clearly) to find the angle that each tangent line
makes with the x-axis.
- Conclude.
Question 3.53)
Differentiate the following functions. Simplify your answers as much as possible.
A) arccos (3x)
B) xsin ¹(x²)
t
sec-1
D) arccsc(-
E) sin (arccot(x²)) (remember to simplify...)
Question 3.54)
Using a chain rule, show how one obtains the derivative of arccosx.
Question 3.55)
A) [sin¯¹(1-r¹)]²
Differentiate the following functions. Simplify your answers as much as possible.
B) cos³ (csc ¹ (²+2)) (remember to simplify...)
C) tan (√r arccos(√r))
cot ¹(x³)
csc(x³)
D)
Question 3.56)
Some "review" questions...
A) Evaluate or simplify the following much as you can.
Show the steps: no calculator, use the definition and properties of logarithms.
i) log 27 (243)
ii) log(2300)-In (23)
iii)
e²ln√x+1
In(10)
B) Solve the following equations for x.
Give both an exact value as well as a decimal approximation from the calculator.
i) 4²x+¹=3.5*
ii) log (In x) = 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2af5a58a-26e3-4baa-9073-1b18b1512b13%2F9c8881b8-713b-43ad-8ce5-596db6d3c40a%2Flbe9dkf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3.51)
Find the value of the following.
Make sure to show the data in the unit circle and/or in right triangles to justify your answers.
A) arcsin (2)
B) arccos (-√2)
C) arctan(-Ys)
D) arccot (cot(-3))
E) sec (arccsc()) (Use a right triangle).
Question 3.52)
Consider the curves y=f(x)=x² and y=g(x)=(x−2)² - 2.
Find the acute angle of intersection between the curves.
Procedure:-Find the point of intersection.
- Find the slope of both tangents lines at that point.
- Use an inverse trigonometric f" (show this clearly) to find the angle that each tangent line
makes with the x-axis.
- Conclude.
Question 3.53)
Differentiate the following functions. Simplify your answers as much as possible.
A) arccos (3x)
B) xsin ¹(x²)
t
sec-1
D) arccsc(-
E) sin (arccot(x²)) (remember to simplify...)
Question 3.54)
Using a chain rule, show how one obtains the derivative of arccosx.
Question 3.55)
A) [sin¯¹(1-r¹)]²
Differentiate the following functions. Simplify your answers as much as possible.
B) cos³ (csc ¹ (²+2)) (remember to simplify...)
C) tan (√r arccos(√r))
cot ¹(x³)
csc(x³)
D)
Question 3.56)
Some "review" questions...
A) Evaluate or simplify the following much as you can.
Show the steps: no calculator, use the definition and properties of logarithms.
i) log 27 (243)
ii) log(2300)-In (23)
iii)
e²ln√x+1
In(10)
B) Solve the following equations for x.
Give both an exact value as well as a decimal approximation from the calculator.
i) 4²x+¹=3.5*
ii) log (In x) = 2
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