#Determining continuity calculus how to#
#Determining continuity calculus full#

§2: Calculus of Functions of Two Variables.§2: The Fundamental Theorem and Antidifferentiation.§11: Implicit Differentiation and Related Rates.§6: The Second Derivative and Concavity.

#Determining continuity calculus how to#

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#Determining continuity calculus full#

For full functionality of this site it is necessary to enable JavaScript. Please e-mail any correspondence to Duane Kouba byĬlicking on the following address About this document. Your comments and suggestions are welcome. Ĭlick HERE to see a detailed solution to problem 15.Ĭlick HERE to return to the original list of various types of calculus problems. Show that f is differentiable for all values of x, but that the derivative, f', is NOT CONTINUOUS at x=0. Show that f is continuous for all values of x. Ĭlick HERE to see a detailed solution to problem 14.

PROBLEM 14 : Show that the following function is continuous for all values of x.

Ĭlick HERE to see a detailed solution to problem 13.

PROBLEM 13 : Determine all values of the constants A and B so that the following function is continuous for all values of x.

Ĭlick HERE to see a detailed solution to problem 12.

PROBLEM 12 : Determine all values of the constant A so that the following function is continuous for all values of x.

PROBLEM 11 : For what values of x is the following function continuous ?Ĭlick HERE to see a detailed solution to problem 11.

PROBLEM 10 : For what values of x is the functionĬlick HERE to see a detailed solution to problem 10.

PROBLEM 9 : For what values of x is the functionĬlick HERE to see a detailed solution to problem 9.

PROBLEM 8 : For what values of x is the functionĬlick HERE to see a detailed solution to problem 8.

PROBLEM 7 : For what values of x is the functionĬlick HERE to see a detailed solution to problem 7.

PROBLEM 6 : For what values of x is the functionĬlick HERE to see a detailed solution to problem 6.

Ĭlick HERE to see a detailed solution to problem 5.

PROBLEM 5 : Check the following function for continuity at x=3 and x=-3.

Ĭlick HERE to see a detailed solution to problem 3.Ĭlick HERE to see a detailed solution to problem 4.

PROBLEM 3 : Determine if the following function is continuous at x=0.

Ĭlick HERE to see a detailed solution to problem 2.

PROBLEM 2 : Determine if the following function is continuous at x=-2.

Ĭlick HERE to see a detailed solution to problem 1.

PROBLEM 1 : Determine if the following function is continuous at x=1.

For a review of limits and indeterminate forms click here. Knowledge of one-sided limits will be required. Mistakes by using the above step-by-step definition of continuity at a point and the well-known facts, and by giving careful consideration to the indeterminate formĭuring the computation of limits. If you are going to try these problems before looking at the solutions, you can avoid common All limits are determined WITHOUT the use of Any polynomial is continuous for all values of x.ħ. The FUNCTIONAL COMPOSITION of continuous functions is continuous at all points x where the composition is properly defined.Ħ.

The QUOTIENT of continuous functions is continuous at all points x where the DENOMINATOR IS NOT ZERO.ĥ. The PRODUCT of continuous functions is continuous.Ĥ.

The DIFFERENCE of continuous functions is continuous.ģ. The SUM of continuous functions is continuous.Ģ. Here is a list of some well-known facts related to continuity :ġ. Function y = f( x) is continuous at point x= a if the following three conditions are satisfied :įunction f is said to be continuous on an interval I if f is continuous at each point x in I. The following problems involve the CONTINUITY OF A FUNCTION OF ONE VARIABLE.