Question

MATHEMATICAL INDUCTION. Help please!! :)
http://prntscr.com/5tukym

Answer 1

ok show its true for first derivative , assume its true for n derivative then induction step to show its true for n+1
i'll skip first 2 step and will go to the third one

Answer 2

yepp okay!

Answer 3

Step 1 is usually to prove true for n= 1 right?
Then assume n= k
Then we're required to prove n= k+1 is also true.. i think?

Answer 4

\(\begin{align*}
\frac{d^{k+1}y}{dx^{k+1}} &= \left (\frac{d^{k}y}{dx^{k}} \right )' \\
&=\left (e^x(x+k) \right )' \\
&= (e^x)'(x+k)+e^x(x+k)'\\
&= e^x(x+k)+e^x \\
&= e^x(x+k+1)
\end{align*}\)

Answer 5

eh u can solve of term of n or k not a matter

Answer 6

hmm alright.
I think i understand it..

Answer 7

eh im here incase u dont

Answer 8

okay so i know the first step is generally to prove true for n=1 right?
And we want to show that LHS = RHS
But i'm not sure what's the LHS and what is the RHS that we're using???

Answer 9

you're inducting on \(n\) here
for the base case, you need to show that the given statement is true for \(n=1\)

Answer 10

ok first step
y=xe^x
u wanna show
y'=e^x(x+1)

Answer 11

you need to show below is true
\[\dfrac{d^1y}{dx^1} = e^x(x+1)\]

Answer 12

ahh okay.
So LHS would be = d/dx (xe^x)
= (1) e^x + e^x (x) THEN use the product rule so:
= (1+ x) e^x
and RHS would be (1+x) e^x ?
So LHS= RHS
therefore, true for n= 1 ?

Answer 13

Looks perfect to me!

Answer 14

yosh

Answer 15

yosh?

Answer 16

eh wio it means yes

Answer 17

she says yosh for yes when eating icecream

Answer 18

Then after that i would.. substitute n=k into
d^n (y) / dx^n = e^x (x +n)
Assume n= k true
i.e d^k y/ dx^k = e^x (x + k)
Then prove n = k+1 is also true (WHICH @Marki proved)
right?

Answer 19

yep u got it

Answer 20

okey dokeys!
Thanks guuuyyss! @Marki enjoy your ice cream??
@ganeshie8 thanks for helping as usual :)

Answer 21

sure rofl