can someone please explain this problem? (-> is an arrow)
assume that limit x-> 4 f(x)=0 and limit x-> 4 g(x)=3
1. limit x-> 4 (g(x)+3
the answer is 21x
how?
To understand and explain this problem, we need to recall some basic concepts related to limits in calculus.
In this problem, we are given the limits of two functions as x approaches 4. The function f(x) has a limit of 0 as x approaches 4, and the function g(x) has a limit of 3 as x approaches 4.
Now, we are asked to calculate the limit of the expression g(x) + 3 as x approaches 4.
To find the limit, we can use the basic properties of limits. One of them states that the limit of the sum of two functions is equal to the sum of their limits. So, we can rewrite the expression as follows:
limit x->4 (g(x) + 3) = limit x->4 g(x) + limit x->4 3
Since we are given that limit x->4 g(x) = 3, we can replace this value in the equation:
limit x->4 (g(x) + 3) = 3 + limit x->4 3
Now, the limit of a constant function (in this case, 3) is simply the value of the constant. So:
limit x->4 (g(x) + 3) = 3 + 3
Simplifying further:
limit x->4 (g(x) + 3) = 6
Therefore, the limit of the expression g(x) + 3 as x approaches 4 is 6.