Finding the Value of b to Make f Continuous at x=0

Thread starter naspek
Start date Dec 13, 2009
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Continuous Value

In summary, a function is continuous at a given point if the limit of the function exists at that point and is equal to the value of the function at that point. It is important to find the value of b that makes f continuous at x=0 because continuity is a fundamental concept in mathematics and is necessary for many mathematical calculations and applications. To determine the value of b, we use the formula b = lim f(x) as x approaches 0. There can be more than one value of b that makes f continuous at x=0, but in most cases, there is only one specific value. Some real-life applications of finding the value of b include analyzing motion and velocity in physics and predicting market trends in economics.

Dec 13, 2009

naspek

f(x) = { [(e^x) - 1] / x ; if x not equal 0
... .{ b ......; if x = 0

What value of b makes f continuous at x = 0?

so.. the left side and right side must be equal in order to make
f continuous at x = 0

[(e^x) - 1] / x = b
[(e^x) - 1] = (b)(x)
e^x = (b)(x) + 1
.
.
.
dont know how to proceed..

should i introduce ln?

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Dec 13, 2009

rochfor1

What is the definition of continuity?

1. What does it mean for a function to be continuous at a given point?

For a function to be continuous at a given point, it means that the limit of the function exists at that point and is equal to the value of the function at that point. In other words, there are no sudden jumps or breaks in the graph of the function at that point.

2. Why is it important to find the value of b that makes f continuous at x=0?

Finding the value of b that makes f continuous at x=0 allows us to determine if the function is continuous at that point. This is important because continuity is a fundamental concept in mathematics and is necessary for many mathematical calculations and applications.

3. How do you determine the value of b to make f continuous at x=0?

To determine the value of b that makes f continuous at x=0, we use the following formula: b = lim f(x) as x approaches 0. This means that we need to take the limit of the function as x approaches 0 and set it equal to b.

4. Can there be more than one value of b that makes f continuous at x=0?

Yes, there can be more than one value of b that makes f continuous at x=0. This is because there can be multiple ways to approach a limit and still get the same result. However, in most cases, there is only one specific value of b that makes the function continuous at x=0.

5. What are some real-life applications of finding the value of b to make f continuous at x=0?

One real-life application of finding the value of b to make f continuous at x=0 is in physics, particularly in the study of motion and velocity. The concept of continuity is essential in understanding the smoothness and flow of motion. Additionally, in economics, continuity is important in analyzing market trends and predicting future values.