Let f ( x ) = { | x | x if x ≠ 0 1 if x = 0 (a) Show that f is continuous at 0. (b) Investigate graphically whether f is differentiable at 0 by zooming in several limes toward the point (0, 1) on the graph of f . (c) Show that f is not differentiable at 0. How can you reconcile this fact with the appearance of the graphs in part (b)?
Let f ( x ) = { | x | x if x ≠ 0 1 if x = 0 (a) Show that f is continuous at 0. (b) Investigate graphically whether f is differentiable at 0 by zooming in several limes toward the point (0, 1) on the graph of f . (c) Show that f is not differentiable at 0. How can you reconcile this fact with the appearance of the graphs in part (b)?
(b) Investigate graphically whether f is differentiable at 0 by zooming in several limes toward the point (0, 1) on the graph of f.
(c) Show that f is not differentiable at 0. How can you reconcile this fact with the appearance of the graphs in part (b)?
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
16. Solve each of the following equations for x.
(a) 42x+1 = 64
(b) 27-3815
(c) 92. 27² = 3-1
(d) log x + log(x - 21) = 2
(e) 3 = 14
(f) 2x+1 = 51-2x
11. Find the composition fog and gof for the following functions.
2
(a) f(x) = 2x+5, g(x) = x²
2
(b) f(x) = x²+x, g(x) = √√x
1
(c) f(x) = -1/2)
9
9(x) =
х
=
-
X
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