CPhill

 y = -1/2x+10     multiply both sides by 2

2y  = -1x + 20    add 1x to both sides

1x + 2y  = 20     this is S.F.     [  Ax + By  = C ]

OK, pokemonking......have a good day.....

The Guest did pretty well, too....!!!!

Since we have  0/0 situations , we can use L'Hospital's Rule in both cases

4. lim    [1 - e^(2x) ] /  sin x       =      lim  [ -2e^(2x)] / cos x  =      -2/1   = -2

   x → 0                                            x → 0

6. lim [sin^2 x ] / [ e^(5x) -1` ]   =     lim  [2sinx cos x] / [5 e^(5x) ]  =  lim  [ sin 2x] / [ 5e^(5x)  ]  =   0/5  = 0

     x → 0                                            x → 0                                             x → 0

Hey....I thought that was pretty good.......HEHEHEHE!!!!

From drunk parents in France.......

Haven't  you ever heard of the "Plastered" of Paris  ??"

Maybe Max can be a "Ginger" Snap......

x^2 - 3|x| + 4 = 0

I don't  believe this has any "real" solutions......

See here :  https://www.desmos.com/calculator/pvwvwzobj7

F(x)=x^3+3x^2+4x+12

Factor to  find the roots

x^2(x + 3) + 4(x + 3)  = 0

(x^2 + 4) (x + 3)  = 0

Set the factors to 0

x^2 + 4  =0                    x +  3  = 0

x^2  = − 4                      x    =  − 3

x = ± i√ 4

x = ± 2i

So.....the roots are ± 2i  and − 3

What is the function with the height in feet from the ground as the independent variable?

let f(x)  = h

h  = −16x^2 + 32

h − 32  = −16x^2        divide by −16

[ h − 32] / − 16   = x^2

[32 − h ] / 16   = x^2  take the positive root of both sides

√[32 − h ] / 4   = x

After about how many seconds were the keys 4 feet above the ground ?

√[32 − 4 ] / 4  =  √[28 ] / 4  =  √[7 ] / 2  sec  ≈ 1.32 sec