Continuity & Differentiability miscellaneous on-line topics for Calculus Applied to the Real World Exercises

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Utility: Function Evaluator & Grapher

1. Let f have the graph shown below.

 f is Select one continuous discontinuous undefined at x = -2 f is Select one continuous discontinuous undefined at x = -1 f is Select one continuous discontinuous undefined at x = 0 f is Select one continuous discontinuous undefined at x = 1 f is Select one continuous discontinuous undefined at x = 2 f is Select one continuous discontinuous undefined at x = 3

2. Let f be specified by

f(x)   =  x if x < -1 xx + 1 if -1 < x 1 x2 if 1 < x 2 x if x > 2
.
 f is Select one continuous discontinuous undefined at x = -2 f is Select one continuous discontinuous undefined at x = -1 f is Select one continuous discontinuous undefined at x = 0 f is Select one continuous discontinuous undefined at x = 1 f is Select one continuous discontinuous undefined at x = 2 f is Select one continuous discontinuous undefined at x = 3

3. Find the values of h and k that make the following function g continuous.

g(x)   =  x2 + h if x < -1 x + 4 if -1 < x 1 xx + k if x > 1
.
 h = k =

4.Here are some multiple choice questions.

(a)
 If f is continuous at the point x = a, then limxa- f(x) is Select one always not always never equal to f(a).
(b)
 If f is not continuous at the point x = a, then limxa- f(x) Select one must may or may not cannot exist.
(c)
 If f is not continuous at the point x = a, then f'(a) Select one must may or may not cannot exist.
(d)
 If f is not differentiable at the point x = a, then f Select one must may or may not cannot be continuous at x = a.

5. Let f have the graph shown below.

 f is Select one differentiable discontinuous continuous but not differentiable undefined at x = -2 f is Select one differentiable discontinuous continuous but not differentiable undefined at x = -1 f is Select one differentiable discontinuous continuous but not differentiable undefined at x = 0 f is Select one differentiable discontinuous continuous but not differentiable undefined at x = 1 f is Select one differentiable discontinuous continuous but not differentiable undefined at x = 2 f is Select one differentiable discontinuous continuous but not differentiable undefined at x = 3

6. Make the appropriate choices below.

 f(x) = (x+1)1/3(x-2)4/3 is Select one not differentiable differentiable undefined at x = -1 f(x) = (x+1)1/3(x-2)4/3 is Select one not differentiable differentiable undefined at x = 2 f(x) = (x+1)2/3(x-2)-1 is Select one not differentiable differentiable undefined at x = -1 f(x) = (x+1)2/3(x-2)-1 is Select one not differentiable differentiable undefined at x = 2 f(x) = |x+1| |x-2|2 is Select one not differentiable differentiable undefined at x = -1 f(x) = |x+1| |x-2|2 is Select one not differentiable differentiable undefined at x = 2

Last Updated:October, 1999