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anonymous
 5 years ago
(a)find y as a function of x, if y'=e^(x1) and y =1 when x=1. What is the y intercept of this curve?
(b)The gradient of a curve is given by y'=e^(2x) and the curve passes through the point (0,1). What is the equation of this curve? What is its horizontal axis?
(c)f=Find y, given that y'=2^(x), and y=1/2log2 when x =0.
(d) It is known that f'(x) = e^x + 1/e and that f(1)=1. Find f(0)
anonymous
 5 years ago
(a)find y as a function of x, if y'=e^(x1) and y =1 when x=1. What is the y intercept of this curve? (b)The gradient of a curve is given by y'=e^(2x) and the curve passes through the point (0,1). What is the equation of this curve? What is its horizontal axis? (c)f=Find y, given that y'=2^(x), and y=1/2log2 when x =0. (d) It is known that f'(x) = e^x + 1/e and that f(1)=1. Find f(0)

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\int\limits e ^{x1}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[1/e \int\limits e^x d x\]

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1a) \[y = \int\limits_{}^{} e ^{x1}dx\] u = x1 du = dx \[y=\int\limits_{}^{}e ^{u}du = e ^{u}+C=e ^{x1}+C\] 1=e^0 +C = 1+C C=0 y = e^x1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i actually did (a) i need help with the other ones more lol

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1b) y = e^2x + C 1=e^2 +C C = 1+e^2 \[y = e ^{2x} +e ^{2}+1\] c) y=2^(x)/ln2 +C 1/2ln2 = 1/ln2 +C C = 3/2ln2 \[y = \frac{1}{\ln 2}(2^{x} \frac{3}{2})\] d) f(x) = e^x + x/e +C 1 = e^1 1/e +C C = 1 f(x) =e^x +x/e 1 f(0) = 11 = 0

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for c is it the same as writing y=12^(x)/log2

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1yeah well i get 3/2 or 1.5 instead of 1 but yes you could write it either way

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thats the answer at the back of the book lol

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1ahh well book must be wrong..:) is it 1/2*ln2 or 1/(2ln2) for initial conditions

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0isnt it the same thing

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1no one the log is on top the other its on the bottom

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1thats what i thought i dont know what i did wrong on that one...

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0when i did it i got c=1/2log2 1/2log2 c=1/2log2+1/2log2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0theres should be no negative infront of y=2^(x)/ln2 +C i think lol

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1wait is x=0 or x=1 ? no there needs to be a neg because derivative of x = 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh sorry i wrote it wrong

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1thats it then lol it says 0 above

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah im sorry lol i must of did it by accident lol

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1it happens, keeps me on my toes :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0lol thanks heaps you made me learn something new today:)

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1your welcome good luck on the rest

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for question (b) when you sub in x = 1 dont you just get e

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1f(x) = e^x + x/e +C when x=1, = e^1 + 1/e +C =1/e  1/e +C =0 + C its not e because e is in denominator

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1oh i was looking at d)...is that right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ur answer is right but i tried doing it on my own and got e :(

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1ok y=−e^(2−x)+e^2+1 x=1 =e^(2(1)) +e^2 +1 =e^3 +e^2 +1 ahh no you cant combine the e's because of the addition

dumbcow
 5 years ago
Best ResponseYou've already chosen the best response.1oh why are you using x=1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0omg whats wrong with me lol im not reading any of the questions right im really sorry for troubling you for no reason
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