3. L7: I can compute average rates of change and find slopes of secant lines. D1: I can explain the purpose of each symbol in the limit definition of derivative. I can illustrate each part of the definition graphically and explain the role of the limit. D5 I can use the limit definition of the derivative to determine the differentiability of a function at a point. Use k(x) = = -2x+6 -2x + 5 x < 2 k(2) -k(1.5)_ 21.5 x ≥ 2 to answer the following questions. (a) Sketch a graph of k(x). (b) (L7) Compute the AROC between x = 1.5 and x = 2: Sketch the secant line with this slope on your graph, using a new texture/color to make it easy to distinguish from k(x). (i.e. use a highlighter/dashed line) Label this line 3b. (c) (L7) Compute the AROC between x = 2.5 and x = 2: k(2.5) - k(2) 2.52 Sketch the secant line with this slope on your graph, using a new texture/color to make it easy to distinguish from k(x). (i.e. use a different colored highlighter/dotted line) Label this line 3c.
3. L7: I can compute average rates of change and find slopes of secant lines. D1: I can explain the purpose of each symbol in the limit definition of derivative. I can illustrate each part of the definition graphically and explain the role of the limit. D5 I can use the limit definition of the derivative to determine the differentiability of a function at a point. Use k(x) = = -2x+6 -2x + 5 x < 2 k(2) -k(1.5)_ 21.5 x ≥ 2 to answer the following questions. (a) Sketch a graph of k(x). (b) (L7) Compute the AROC between x = 1.5 and x = 2: Sketch the secant line with this slope on your graph, using a new texture/color to make it easy to distinguish from k(x). (i.e. use a highlighter/dashed line) Label this line 3b. (c) (L7) Compute the AROC between x = 2.5 and x = 2: k(2.5) - k(2) 2.52 Sketch the secant line with this slope on your graph, using a new texture/color to make it easy to distinguish from k(x). (i.e. use a different colored highlighter/dotted line) Label this line 3c.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. L7: I can compute average rates of change and find slopes of secant lines.
D1: I can explain the purpose of each symbol in the limit definition of derivative. I can illustrate
each part of the definition graphically and explain the role of the limit.
D5 I can use the limit definition of the derivative to determine the differentiability of a function
at a point.
Use k(x) =
-2x + 6 x < 2
-2x+5 x ≥ 2
(a) Sketch a graph of k(x).
(b) (L7) Compute the AROC between x = 1.5
and x = 2:
k(2) -k (1.5)_
21.5
to answer the following questions.
Sketch the secant line with this slope on your graph, using a new texture/color to make it
easy to distinguish from k(x). (i.e. use a highlighter/dashed line) Label this line 3b.
(c) (L7) Compute the AROC between x = 2.5 and x = 2:
●
Sketch the secant line with this slope on your graph, using a new texture/color to make it
easy to distinguish from k(x). (i.e. use a different colored highlighter/dotted line) Label this
line 3c.
(d) (D5) The limit definition for k' (2) = lim
k(2+ h) — k(2)
h
"
h→0
but because k is defined piecewise
and x = 2 is the split, we need to use two one-sided limits to explore k' (2). Compute the
limits below, then use the graph and your secant lines to double check your work. Remember
the fixed point (2, k(2)) is fixed and doesn't change as h changes.
lim
h→0-
k(2.5) - k(2)
2.5-2
k(2+h)-k(2)
h
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