Find g(4) When f(4)-5 and lim[5f(x)-g(x)]=5

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SUMMARY

The discussion centers on finding the value of g(4) given that f(4) = 5 and the limit lim[5f(x) - g(x)] as x approaches 4 equals 5. Participants emphasize the importance of understanding limit rules and the behavior of continuous functions within limits. The confusion regarding the notation and presentation of the problem is highlighted, suggesting that clarity is essential for effective problem-solving. Ultimately, the manipulation of the limit equation using algebraic rules is crucial to derive g(4).

PREREQUISITES
  • Understanding of limit rules in calculus
  • Knowledge of continuous functions
  • Familiarity with algebraic manipulation of equations
  • Basic comprehension of function notation and symbols
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  • Study the properties of continuous functions in calculus
  • Learn about limit laws and their applications
  • Practice algebraic manipulation of limits with examples
  • Explore common pitfalls in presenting mathematical problems clearly
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Students and educators in calculus, mathematicians dealing with limits, and anyone seeking to improve their problem presentation skills in mathematical discussions.

step1536
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If f and g are continuous functions with f(4)-5 and lim [5f(x) -g(x) ]=5 find g(4)
x-->4
 
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It's a bit tough to read what's going on here

Is this supposed to be f(4)=5? the limit as x goes to 4 of [5f(x)-g(x)]=5? And you want to find g(4)?

If so, you should be able to manipulate your limit equation using algebra of limit rules (for example, lim(a+b) = lim(a) + lim(b)). Then you need to know what happens to a continuous function when you have it inside of a limit. What do you think happens?
 


step1536 said:
If f and g are continuous functions with f(4)-5 and lim [5f(x) -g(x) ]=5 find g(4)
x-->4

Aside from the confusion over whether you're saying that f(4) = -5 or f(4) = 5, do you want g(4) or [itex]\lim_{x \rightarrow 4} g(x)[/itex]?

If you want to get help, you really need to concentrate on presenting your problem so that people can understand what you're asking. That would include spending some time on learning what the relevant symbols mean.
 

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