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nDeriv is on my calculator, when we want the calculator to derive.
here is translated what is standing in the answer:
if y=a^x, then you get the base a that is such as y'(1)=a
Solve (nDeriv(a^x, x, 1) -a, a, 2) gives a≈2,718
in the last one i think you must come up with two equations and then you must break out 1 variable and put in that equation in the other one. so if you break out "x" in one equation you put the whole expression in the other equation, where it is x.
try it, maybe i'm wrong.
okay thx.. if anyone could help me with the second problem that would be awesome. a should be e and i see why because k=1 but i still can't understand how to solve it.
deriving from the derive definition of f(x)=√x you do like this:
(f(x+h)-f(x)/h) = √(x+h)-√(x)/h, then you multiply with (√(x+h)-√(x)) making it all (√(x+h)+√(x))*(√(x+h)-√(x)) / h*(√(x+h)+√(x)) = (x+h-x) / (h*(√(x+h)+√(x))) = 1 / (√(x+h)+√(x)).
then we make h go towards zero.
f'(x)=lim_h-->0(1/(√(x+h)+√(x)) = 1 / (√(x) + √(x)) = 1 / 2*√(x)
f(x)=√(x) gives f'(x)= (1/(2√(x)))
1²=1
2²=4
3²=9
4²=16
5²=25
6²=36
7²=49
8²=64
9²=81
10²=100
...
1582²=2502724
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hint: n²=(n-(n-1)+n)
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do you see a pattern?
i see two!
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try to find the other formula.
the formula should be easy to use without a calculator allowing one to solve one's potens problems without any problems.
1) find all solutions to the equation:
x^(lg_x)=(x^(3/100))
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2) what do you get when solving the equation:
nDeriv(a^x, x, 1)=a
with attention to a?
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3) how do we derive i.e. y=7^x? the answer is that we change the base e this way:
if 7=e^z, then z=log_e(7) ⇒ 7=e^(log_e(7))
this is the only example in the book and i can't understand the method. please explain a little simplier.
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these three problems i really need help with.
if you don't understand the question please let me know 'cause i'm not a native english speaker.
ps: i have the answer to the first 2 problems, but i need to understand every step into detail.
Pages: 1