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1.7. LIMITS, CONTINUITY, AND DIFFERENTIABILITY
(b) Use the limit definition of the derivative to show that
g
′ (0) = lim
h→0
|h|
h
.
(c) Investigate the value of g ′ (0) by estimating the limit in (b) using small positive
and negative values of h. For instance, you might compute
√
|−0.01|
0.01 . Be sure to
use several different values of h (both positive and negative), including ones
closer to 0 than 0.01. What do your results tell you about g ′ (0)?
(d) Use your graph in (a) to sketch an approximate graph of y = g ′ (x).
1.7. LIMITS, CONTINUITY, AND DIFFERENTIABILITY
(b) Use the limit definition of the derivative to show that
g
′ (0) = lim
h→0
|h|
h
.
(c) Investigate the value of g ′ (0) by estimating the limit in (b) using small positive
and negative values of h. For instance, you might compute
√
|−0.01|
0.01 . Be sure to
use several different values of h (both positive and negative), including ones
closer to 0 than 0.01. What do your results tell you about g ′ (0)?
(d) Use your graph in (a) to sketch an approximate graph of y = g ′ (x).