Chapter 2: Q. 2 TB (page 208)
For each function k that follows, find functions f , g, and h so that k = f ◦ g ◦ h. There may be more than one possible answer.
Short Answer
Ifandthen
If and then
If and then
If and then
Chapter 2: Q. 2 TB (page 208)
For each function k that follows, find functions f , g, and h so that k = f ◦ g ◦ h. There may be more than one possible answer.
Ifandthen
If and then
If and then
If and then
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Get started for freeuse the definition of derivative to directly prove the differentiation rules for constant and identity function
Taking the limit: We have seen that if f is a smooth function, then This approximation should get better as h gets closer to zero. In fact, in the next section we will define the derivative in terms of such a limit.
.
Use the limit just defined to calculate the exact slope of the tangent line toat
Use (a) the definition of the derivative and then
(b) the definition of the derivative to find for each function f and value in Exercises 23–38.
23.
For each function f and value in Exercises 35–44, use a sequence of approximations to estimate . Illustrate your work with an appropriate sequence of graphs of secant lines.
In Exercises 69–80, determine whether or not is continuous and/or differentiable at the given value of . If not, determine any left or right continuity or differentiability. For the last four functions, use graphs instead of the definition of the derivative.
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