Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 57SE: Repeat the previous exercise to find the formula forthe APY of an account that compounds daily....
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I'm seeking help on the 2nd bullet point starting with "Now find the equation of the tangent line..."
![For this process we'll use the function f (x) = x² - 2.
For a
2, and the interval [2, 3], find each of the following without actually
calculating the equation of the tangent line, explaining how you do so, and illustrating
them on your graph (using screenshot annotation tools, for example, or some other
method). Zoom in enough to make sure each the quantities are shown clearly!
Ax
dx
Ay
dy
Now, find the equation of the tangent line at a = 2, and the equation of the secant
line for the interval [2, 3]. Add these two lines to your graph, and illustrate the
quantities Ax, dx, Ay, dy again. Explain the relationships between these quantities
and the tangent line and secant line.
For the same function, without calculating anything, sketch an illustration of the
Newton's Method process for finding the ₁ and 2 approximations of the zero of the
function, using the seed value o = 2. (Draw in the lines that would produce the next
two approximations after this initial value.) Explain how each line produces the next
approximation.
Now use the Newton's Method formula to find ₁ and ₂. How do they compare
to your illustration?
Because you already found the tangent line at x = 2 in an earlier problem, use it
to verify the ₁ value you got using the formula.
Hamil
Sign ou](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2Feac3b10d-26e0-4f2d-b515-763c8f7ccade%2F5y8yb7q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For this process we'll use the function f (x) = x² - 2.
For a
2, and the interval [2, 3], find each of the following without actually
calculating the equation of the tangent line, explaining how you do so, and illustrating
them on your graph (using screenshot annotation tools, for example, or some other
method). Zoom in enough to make sure each the quantities are shown clearly!
Ax
dx
Ay
dy
Now, find the equation of the tangent line at a = 2, and the equation of the secant
line for the interval [2, 3]. Add these two lines to your graph, and illustrate the
quantities Ax, dx, Ay, dy again. Explain the relationships between these quantities
and the tangent line and secant line.
For the same function, without calculating anything, sketch an illustration of the
Newton's Method process for finding the ₁ and 2 approximations of the zero of the
function, using the seed value o = 2. (Draw in the lines that would produce the next
two approximations after this initial value.) Explain how each line produces the next
approximation.
Now use the Newton's Method formula to find ₁ and ₂. How do they compare
to your illustration?
Because you already found the tangent line at x = 2 in an earlier problem, use it
to verify the ₁ value you got using the formula.
Hamil
Sign ou
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