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.)
We can set up 2 equations given the information.
Let the price of advance ticket be represented by A and same day ticket by S
A + S = 50
20A + 40S = 1700
Solve for A in the first equation by subtracting S on both sides.
U will get A = 50 - S
Now substitute 50 - S for A in the second equation.
20 (50 - S) + 40S = 1700
1000 - 20S + 40S = 1700
20S = 700
S = 35
Same day ticket costs $35 and advance ticket costs $15
Answer:
18 years
Step-by-step explanation:
2(8+x) = 34+x
16+2x = 34+x
-18 = -x
◆ Define the variables:
Let the calorie content of Candy A = a
and the calorie content of Candy B = b
◆ Form the equations:
One bar of candy A and two bars of candy B have 774 calories. Thus:
a + 2b = 774
Two bars of candy A and one bar of candy B contains 786 calories
2a + b = 786
◆ Solve the equations:
From first equation,
a + 2b = 774
=> a = 774 - 2b
Put a in second equation
2×(774-2b) + b = 786
=> 2×774 - 2×2b + b = 786
=> 1548 - 4b + b = 786
=> -3b = 786 - 1548
=> -3b = -762
=> b = -762/(-3) = 254 calorie
◆ Find caloric content:
Caloric content of candy B = 254 calorie
Caloric content of candy A = a = 774 - 2b = 774 - 2×254 = 774 - 508 = 266 calorie
