Question

Given: lim g(x)=4, g'(5) = -1
x->5

Continuous at x=5

Find the value of the following;

lim [g(x)-g(5)]
x->5

Answer 1

I guess my question is whether g(5) = g'(5). I assume not, which leads me to the question: how the heck do you find out the value of g(5)?

Answer 2

It is given that g is continuous at 5. So does not this mean that g(5)=lim as x approaches 5 of g?

Answer 3

would it not mean that you would take the antiderivative of -1 and then plug 5 in which would give you the point 9?

Answer 4

i could be wrong

Answer 5

^ Never done anti-derivatives.

Answer 6

hmm...

Answer 7

I am fairly certain g(5)=4

Answer 8

this would mean the solution is 0

Answer 9

wait is it saying in the given that the lim as x approaches 5 of g(x) is 4? if so then yes i believe the answer is 0 as well

Answer 10

thats what I assumed

Answer 11

that is what it appears to be

Answer 12

giving g'(x)=-1 is just unnecessary information

Answer 13

^ There were six questions given the same information. only needed help with 1/6

Answer 14

So Dong, what you were saying above is g(5) = 5 because the functions are continuous at x=5?

Answer 15

"wait is it saying in the given that the lim as x approaches 5 of g(x) is 4? if so then yes i believe the answer is 0 as well"

I missed this post. Yes, it is saying that.

Answer 16

no he is saying that since the limit as x approaches 5 for g(x) is 4 and to get that you have to plug 5 into the equation that you cannot see then by assumption g(5) is the same thing as g(x) based on the limit. that would make the limit as x approaches 5, 4-4

Answer 17

i believe that is what he was saying

Answer 18

Thank you for the clarification and help, both of you :)

Answer 19

no prob! :D