3. What is the solution of the following
2 answers:
You might be interested in
Answer:
f'(1)=150ln(1.5)
Step-by-step explanation:
I'm not sure why you would need a table since the limit definition of a derivative (from what I'm remembering) gives you the exact formula anyway... so hopefully this at least helps point you in the right direction.
My work is in the attachment but I do want to address the elephant on the blackboard real quick.
You'll see that I got to the point where I isolated the h's and just stated the limit equaled the natural log of something out of nowhere. This is because, as far as I know, the way to show that is true is through the use of limits going to infinity. And I'm assuming that you haven't even begun to talk about infinite limits yet, so I'm gonna ask you to just trust that that is true. (Also the proof is a little long and could be a question on it's own tbh. There are actually other methods to take this derivative but they involve knowing other derivatives and that kinda spoils a question of this caliber.)
Answer:
Option B)
Step-by-step explanation:
The given geometric sequence is
2, 8, 32, 128,....
The general form of a geometric sequence is given by
Where n is the nth term that we want to find out.
a₁ is the first term in the geometric sequence that is 2
r is the common ratio and can found by simply dividing any two consecutive numbers in the sequence,
You can try other consecutive numbers too, you will get the same common ratio
So the common ratio is 4 in this case.
Substitute the value of a₁ and r into the above general equation
This is the general form of the given geometric sequence.
Therefore, the correct option is B
Note: Don't multiply the first term and common ratio otherwise you wont get correct results.
Verification:
Lets find out the 2nd term
Substitute n = 2
Lets find out the 3rd term
Substitute n = 3
Lets find out the 4th term
Substitute n = 4
Lets find out the 5th term
Substitute n = 5
Hence, we are getting correct results!