The goal of this problem is to compute the value of the derivative at a point for several different functions, where for each one we do so in three different ways, and then to compare the results to see that each produces the same value. For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. Note: At least one graph will have a derivative that does not exist so please enter DNE ƒ(x) = x² − 6x, a = 4 f(x) f(x) = f(x) = 1 = x " a = - 4 Note: the lim sin(x), a = π 2 sin (h) h h→0 √x, a = 1 Hint = 1 and the lim 1 h→0 f(x) = 7 x − 4|, a = 4 cos(h) h = 0
The goal of this problem is to compute the value of the derivative at a point for several different functions, where for each one we do so in three different ways, and then to compare the results to see that each produces the same value. For each of the following functions, use the limit definition of the derivative to compute the value of f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph of y = f(x) near (a, f(a)) visually. Compare your findings among all three approaches; if you are unable to complete the algebraic approach, still work numerically and graphically. Note: At least one graph will have a derivative that does not exist so please enter DNE ƒ(x) = x² − 6x, a = 4 f(x) f(x) = f(x) = 1 = x " a = - 4 Note: the lim sin(x), a = π 2 sin (h) h h→0 √x, a = 1 Hint = 1 and the lim 1 h→0 f(x) = 7 x − 4|, a = 4 cos(h) h = 0
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
Please answer fast i will rate for
Transcribed Image Text:The goal of this problem is to compute the value of the derivative at a point for several different functions,
where for each one we do so in three different ways, and then to compare the results to see that each
produces the same value.
For each of the following functions, use the limit definition of the derivative to compute the value of
f'(a) using three different approaches: strive to use the algebraic approach first (to compute the limit
exactly), then test your result using numerical evidence (with small values of h), and finally plot the graph
of y = f(x) near (a, f(a)) visually. Compare your findings among all three approaches; if you are unable
to complete the algebraic approach, still work numerically and graphically.
Note: At least one graph will have a derivative that does not exist so please enter DNE
ƒ(x) = x² − 6x, a = 4
f(x)
f(x)
=
f(x)
=
1
=
x
"
a = - 4
Note: the lim
sin(x), a =
π
2
sin (h)
h
h→0
√x, a = 1
Hint
= 1 and the lim 1
h→0
f(x) = 7 x − 4|, a = 4
cos(h)
h
= 0
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
