Find g(4): Solving the Limit Equation

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In summary, the conversation discusses finding the value of g(4) in a problem involving continuous functions f and g. The solution involves rewriting the problem and using direct substitution to find the limit of fx, which is equal to 1. Then, by replacing 1 with the limit of fx, the limit of gx can be found. However, the speaker made an error in their calculation and the correct value for g(4) is not 5/4.
  • #1
Rasine
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If f and g are continuous functions with f(4)=1 and lim x-> 4 (6fx - gx)= 1 find g(4)

i cam rewrite this as lim x-> 4 (6f) - lim x-> 4 gx =1

so i know that fx is defined at 4 so it has a limit and that by direct substution the limit of fx= 1

so if i replace 1 with the lim of fx i have 1- lim x-> 4 gx=1

and by using direct subustion again i can find g(4) which is the limit of gx

i solve and get 5/4 for the lim of gx which should be g(4) but that is not right

can someone please tell me where i am going wrong?
 
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  • #2
How did you get 5/4?
 
  • #3
n/m i just noticed what i was doing wrong
 

1. What is the meaning of "g(4)"?

"g(4)" refers to the value of the function g at the input or independent variable of 4. It is the output or dependent variable that is produced when the input is 4.

2. How is the limit equation used to find g(4)?

The limit equation is used to find g(4) by taking the limit of the function g as the input approaches 4. This means that we are finding the value that the function approaches as the input gets closer and closer to 4.

3. What is the process for solving the limit equation to find g(4)?

The process for solving the limit equation to find g(4) involves plugging in the value of 4 for the input in the function g and simplifying the resulting expression. If the function is continuous at 4, then the limit will be equal to the function value at 4. If the function is not continuous at 4, then further steps may be needed to evaluate the limit.

4. Can the limit equation be used to find g(x) for any value of x?

Yes, the limit equation can be used to find g(x) for any value of x. The process is the same as finding g(4), but instead of plugging in 4 for the input, you would plug in the desired value for x.

5. What is the significance of finding g(4) using the limit equation?

Finding g(4) using the limit equation allows us to determine the behavior of the function g at the input of 4. It can also help us understand the continuity and differentiability of the function at that point. Additionally, it can be used to solve more complex problems or evaluate other mathematical concepts that involve the function g at the input of 4.

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