Next x = 0, the tangent line approxumation gives 7e-5x The figure below shows f(

Question

Next x = 0, the tangent line approxumation gives 7e-5x The figure below shows f(x) and its local linearization at x = a, y = 5x - 5. What is the value of a? a = What is the value of a? a = What is the value of f(a)? f(a) = Use the linearization to approximate the value of f(2.5). f(2.5) = Using a calculate or compute, generate a graph like the ine shown below by graphing y = sin x and y = x for -1 x 1. (What is the relationship between y = sin x and y = x?) Use your graph to estimate to one decimal place the (largest) magnitude of the error in approximating sin x by x for -1 x 1. Find the tangent line approximation for 8 + x near x = 5

Explanation / Answer

Local linearization is where you use the tangent line as an estimate of the function, when you are very close to the tangent point.

1) What is the value of a?
a is the x coordinate of the tangent point. So a= 1

2) What is the value of f(a)? f(1)= 1, which you can see on the graph as (1,1)

3) Use the linearization to approximate the value of f(16)?
Using this tangent line , y= 3(16)-2= 46

4)Is the approximation an under- or overestimate?
Since the function will be way above the tangent line by the time x= 16, this is an underestimate, and not a good use of linearization.
If you meant f(1.6) then 3(1.6)-2= 2.8, which is still an underestimate.

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.