Find the Value of f(5) to Make f(x) Continuous at x=5

In summary, the conversation discusses finding horizontal asymptotes, determining values for a function to make it continuous, and solving for a removable discontinuity. The participants also express confusion and ask for clarification on certain concepts.
  • #1
asdfsystema
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41. Find the Horizontal Asymptotes for17x/(x^4+1)^1/4 The answer I got is 17 and –17 . Can anyone correct me if I’m wrong?

62. f(x)= 4x^3+13x^2+11x+24 / x+3 when x<-3f(x)= 3x^2+3x+A when -3 less than or equal to xWhat is A in order for it to be continuous at -3?I don’t understand the top function but the bottom function I know is that I need to figure out the top and then make it equal to each other to find what A is since it only needs direct substitution

79. f is continuous at (-inf, + inf)f(y) = cy+3 range is (-inf,3)f(y) = cy^2-3 range is (3,+inf)what is C?C= 1 Am I correct?I did c(3)+3 and c(3^2)-3 and set them equal to each other and got 1.

81. Let f(x) = {2x^2+3 x -65) / (x-5)Show that f(x) has a removable discontinuity at x=5 and determine what value for f(5) would make f(x) continuous at x=5.Must define f(5)=The answer is 23? First I factored it and made it into 2x+13 and used direct substitution.Thanks for yoru time !
 
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  • #2
Bump (10char) help please, this is dealing with asymptotes, polynomials and basically limits.
 

What does it mean to find the value of f(5) to make f(x) continuous at x=5?

This means that we are looking for the specific value of the function at x=5 that will make the function continuous at that point. A function is considered continuous at a certain point if the limit of the function at that point is equal to the actual value of the function at that point.

Why is it important to find the value of f(5) to make f(x) continuous at x=5?

It is important to find this value because it ensures that the function is well-defined and has no breaks or gaps at x=5. This allows us to accurately analyze and make predictions based on the function's behavior at that point.

How do I find the value of f(5) to make f(x) continuous at x=5?

To find this value, we need to use the concept of limits. We can set up a limit expression where x approaches 5, and then solve for the value of the limit that will make the function continuous at x=5.

What happens if I cannot find the value of f(5) to make f(x) continuous at x=5?

If we are unable to find the value of f(5) that makes the function continuous at x=5, then the function is not continuous at that point. This means that there is a break or gap in the function at x=5, and we need to further analyze the function to determine how to make it continuous at that point.

Can I use the value of f(5) to make f(x) continuous at other points?

The value of f(5) that makes the function continuous at x=5 may not necessarily make the function continuous at other points. We need to find the specific value of the function at each point where we want it to be continuous. However, the process of finding the value of f(5) can help us understand how to find the values at other points to make the function continuous.

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