lim (2e^(x-5))-2
---------------
x-4
x->5
lim as x approaches 5
(2e^(x-5))-2/x-4
stuck...
plug in 5 for x and solve!
To find the limit of the given expression as x approaches 5, we can try to directly substitute 5 into the expression. However, we encounter an indeterminate form of 0/0. So we need to use a different method, such as algebraic manipulation or L'Hopital's rule.
Let's start by simplifying the expression:
lim(x->5) [(2e^(x-5))-2] / (x-4)
Step 1: Factor out the common factor of (x-5) from the numerator:
lim(x->5) [(2e^(x-5))-2] / (x-5)(x-4)
Step 2: Now that we've factored out the common factor, we can cancel out the (x-5) terms in the numerator and denominator:
lim(x->5) [2e^(x-5) - 2] / (x-4)
Step 3: Now, we can plug in x = 5 into the simplified expression:
[2e^(5-5) - 2] / (5-4)
e^(0) is equal to 1, so the expression becomes:
[2 * 1 - 2] / 1
2 - 2 = 0, so the final answer is 0. Therefore, the limit of the given expression as x approaches 5 is 0.