Calculus 1 final exam limit!

Math, but fast!
#math #algebra #calculus #trig

[MonsterusCow]

duel weilding markers like that is insane

[ShaunakDesaiPiano]

I love how the answer being 5 makes it look like the 5 in the first square root has something to do with it when in fact it’s just a coincidence.

[KingGisInDaHouse]

When radicals are infinity inside you can normally add constants to them without an issue. Because the proprogated error vanishes to zero.

lim x->inf |x+8|-|x+3| // the absolute value sign can be disregarded because the inside is already positive.
lim x->inf x+8-x-3=5

[fibroidss]

Love how you just spoke mandarin at the end of the clip!!!

[TheDannyAwesome]

really interesting! I did it by completing the square, you get the first surd is about ( x + 8 ) and the second surd is about ( x + 3 ) up to lower order terms, so the limit should be 8 - 3 = 5

[Jnsystems]

Extra Credit: Decode what BpRp said after boxing the solution. 😅

[piotrek]

No professor is going to put as easy of a problem as this on a test

[DTLRR]

Can someone explain to me what happened in the second step? How did he ignore the other terms or is it that x is too large for other terms?

[Abandon_rishi]

Words can't describe how grateful I'm.❤

[MT-cfms]

physics teacher giving us something like this or even more complicated in the test yesterday (I'm in 11th grade)

[anthonypham]

You should divide the numerators and denominators by x and then substitute to be more rigorous

[mbmillermo]

Does this work?: → (x+8)-(x+3) = 5. It seems sensible but informal.

[nickronca]

no way, I did it differently and still got it right!

[haddadosama]

If everything in the last step were equal x because x->inf. Why not doing it in the first step and the answer becomes: x-x= zero?

[gonzalotapia]

How I'd solve it
Step 1. Complete the square. Just halve the value of B (ax²+bx+c =0)
We have sqrt((x+8)²-59) - sqrt((x+3)²-9)
Step 2. Discard the constants. They are negligible at the infinite limit.
Sqrt((x+8)²)-sqrt((x-3)²)
Step 3. Remove square roots. Take only the principal root.
(x+8)-(x-3)
Step 4. Clean up the mess
x-x+8-3 = 5
Step 5.???
Step 6. Profit

[chibearsfan]

How does he get from the first formula to the second formula? A lot changed with no work shown.

[merkov]

Input it on the calculator, pres CALC, put 10 9's as the value of X, press equal sign. Done.

[SylveonSimp]

What do I have to do to get rid of the roots in the denominator, if I want to show complete work?

[kumarvishalsinha]

What exactly did he do in the denominator?

Can anyone give me a walkthrough or make me understand what were the sub steps that were applied to come to that conclusion so that both roots becomes "X"

[YRO.]

Idk why, but I hate multiplying by conjugates.