Shown beside is a curve called "lemniscate", given by 2(x² + y²)² = 25(x² - y²). A) Use implicit differentiation to obtain that dyx 50-8(x² + y²) dx y 50+8(x² + y²) B) Verify that the point (3,1) belongs to the lemniscate and find the equation of the line tangent to the curve at this point. ***** Po x wa
Shown beside is a curve called "lemniscate", given by 2(x² + y²)² = 25(x² - y²). A) Use implicit differentiation to obtain that dyx 50-8(x² + y²) dx y 50+8(x² + y²) B) Verify that the point (3,1) belongs to the lemniscate and find the equation of the line tangent to the curve at this point. ***** Po x wa
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Can you please answer question 3.71
![Question 3.61)
Verify the Mean Value Theorem (find that 'c' that is supposed to exist) for the function f(x)=√x on
the interval [0,9].
Question 3.62)
Use the corollary to the IVT and Rolle's Theorem to show that the function p(x)=x² - 4x³−8x² +29
has a unique root in the interval (1,4).
Question 3.71)
Shown beside is a curve called "lemniscate", given by
2(x² + y²)² = 25(x² − y²).
A) Use implicit differentiation to obtain that
dy x 50-8(x² + y²)
dx y 50+8(x² + y²)
B) Verify that the point (3,1) belongs to the lemniscate and
find the equation of the line tangent to the curve
at this point.
Question 3.72)
Consider the rotated ellipse x² - xy + y² = 108 shown beside.
dy
A) Use implicit differentiation to find an expression for
dx
B) Find the coordinates (x, y) of the points on the ellipse
where the tangent line is horizontal.
-2
Question 3.73)
Find the derivative of the following functions, which have x showing both in the base and in the
exponent... Simplify when appropriate.
A) y=(√x) ¹²
B) (In x) x
C) (1+¹)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2af5a58a-26e3-4baa-9073-1b18b1512b13%2F29c2f575-4a0e-4a2f-942a-45a398fb5d34%2Fpbod0pj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 3.61)
Verify the Mean Value Theorem (find that 'c' that is supposed to exist) for the function f(x)=√x on
the interval [0,9].
Question 3.62)
Use the corollary to the IVT and Rolle's Theorem to show that the function p(x)=x² - 4x³−8x² +29
has a unique root in the interval (1,4).
Question 3.71)
Shown beside is a curve called "lemniscate", given by
2(x² + y²)² = 25(x² − y²).
A) Use implicit differentiation to obtain that
dy x 50-8(x² + y²)
dx y 50+8(x² + y²)
B) Verify that the point (3,1) belongs to the lemniscate and
find the equation of the line tangent to the curve
at this point.
Question 3.72)
Consider the rotated ellipse x² - xy + y² = 108 shown beside.
dy
A) Use implicit differentiation to find an expression for
dx
B) Find the coordinates (x, y) of the points on the ellipse
where the tangent line is horizontal.
-2
Question 3.73)
Find the derivative of the following functions, which have x showing both in the base and in the
exponent... Simplify when appropriate.
A) y=(√x) ¹²
B) (In x) x
C) (1+¹)*
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