SOLUTION: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE

Question 1118241: Use a graph of f or some other method to determine what, if any, value to assign to f(a) to make f continuous at x = a. HINT [See Example 2.] (If there is no such value, enter NONE.)
f(x) = 2-2e^x/x; a=0

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

A couple of preliminary comments....

(1) Do you really think it is any help to us to include "HINT [See Example 2.]" in your message to us?!

(2) The problem as you show it is of little interest, because it is impossible to define f(a) to make f continuous at x=0:

which is undefined.

If you are working on a problem like this, then your knowledge of mathematics should be sufficient that you would know appropriate use of parentheses is critical.

The function you are asking about is, in fact, ; not .

At x=0, the function value is the indeterminate form 0/0.

So use l'Hospital's rule.

limit as x approaches 0 of

is equal to

limit as x approaches 0 of = -2e^0 = -2

A graphing calculator will confirm this answer.

RELATED QUESTIONS
Use a graph of f or some other method to determine what, if any, value to assign to f(a)... (answered by MathLover1)

Use a graph of f or some other method to determine what, if any, value to assign to f(a)... (answered by tinbar)

Please help with the following: 1. Is the graph of f(x) = x^1171−5x^109 +3... (answered by richard1234)

Let f be the function defined by f(x)=(cx-(5x^2))/((2x^2)+ax+b), where a, b, and c are... (answered by solver91311)

Suppose f is a linear function and f(x)varies at a constant rate of change of 1.5 with... (answered by solver91311)

If a function is defined to be f(x)= x^4cos(2/x) for x not equal to 0 , then what should... (answered by robertb)

Let f: R to R be a function. Show that if f is continuous on [0,infinitive) and... (answered by khwang)

List the possible rational zeros the function f(x) = {{{3x^3-21x+18}}}? Describe and use... (answered by josgarithmetic)

Suppose that f(x)= (5x) _________ (x^2)−x−6 (that is supposed to... (answered by josgarithmetic,lwsshak3)