Find a and b if f(x) is continuous everywhere

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In this video , I showed how to use to the continuity coondition to find unknowns for a piecewise function

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I LOVE YOU PRIME NEWTONS!! i got a floor functions question on my maths test and knew exactly how to solve it

maxamoyal

Thank you, Newton, I was really struggling with these types of problems. Big respect ✊🏽

teddy

More Calc 2 content please🥺
You’re the best❤

safiaatou

Thank you, thank you, thank you (south africa)

thinz

For f(x) to be continuous everywhere, the lim x-->-2 must exist aka lim x-->-2 (ax^2+bx)= lim x-->-2 (ax^3-10b)= (-7x-2)=14. Therefore, a(-2)^2+b(-2)=14=a(-2)^3-10b by plugging in x=-2 or 4a-2b=14 and -8a-10b=14 as well. Dividing the second equation by -2 gives 4a-2b=14 and 4a+5b=-7 and subtracting the second from the first gives (4a-2b)-(4a+5b)=14-(-7)--> -7b=21 or b=-3. Then plugging b=-3 into equation 1 gives 4a-2(-3)=14 or 4a-(-6)=14 or 4a=8 so a=2. Therefore (a, b)=(2, -3) for f(x) to be continuous everywhere.

jacobgoldman

Thenkss sir ❤❤❤❤ U so muchhh, ( 🇲🇼🇲🇼 know as warm heart of Africa)!!

wlndics

I love your introduction of your videos

bertindiaz

Nice example and work through. What type of chalkboard you use?

TranquilSeaOfMath

When studying computer graphics many years ago, I recall the importance of C2 continuity for creating smooth curves and surfaces. Perhaps you could extend this problem to a C2 function?

MrR

I really like this type of exercise! For fun, I also tried making the first derivative continuous (removing the middle definition, that is redundant), but the solution was the identically zero function 🙃

davidcroft

Keep on doing good work...u make our life

NandiMazibuko-blub

The first one that I see this kind of function . Thank you very much. Bye.

mohamedmehdi

Why the limes evaluation? Just insert the value at "x = -2" into the two formulars together with the x and solve the simple linear two equations! The derivatives we would need if we would want the crossover to become smooth in the derivatives. But that would require a few more degrees of freedom for our functions.

WhiteGandalfs

If the question was phrased “Find the values of a and b for which f is differentiable everywhere” we were gonna different values of a and b which satisfy continuity and differentiability.

maburwanemokoena

thank you so much for the help king! loved it

humnarizwan

Oh, you made it continuous but not differentiable.

Taric

4a-2b=14; -8a-10b=14
12a+8b=0
a=(-2/3)b
(-14/3)b=14
b=-3
a=2

maxvangulik

OR, TO SAY IT DIFFERENTLY, WHEN YOU BUILD THE FUNCTION GRAPH, YOUR HAND SHOULD NOT BE INTERRUPTED DURING DRAWING IT!

klementhajrullaj

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