CPhill

a.) t0 = 1

[f(t)- f(t0)] / [ t - t0 ] =  

[√(4t)  - √ (4*1)] / [t - 1]  =

[ √(4t) - √(4)] / [ t - 1]  =

[ 2 √(t) - 2] / [t - 1]  =

2 [√(t) - 1] / [t - 1]  =

2[√(t) - 1] / [ (√(t) - 1) (√(t) + 1) ]  =

2 / (√(t) + 1)                     

b.) t0= 4

[√(4t)  - √ (4*4)] / [t - 4] =

[ √(4t)  - √(16)] / [ t - 4] =

[ 2 √(t) - 4 /  [t - 4]  =

2 [√(t)  - 2] / [t - 4]  =

2 [√(t)  - 2] /   [ (√(t)  - 2) (√(t)  + 2) ] =

2 / (√(t)  + 2)   

2x^2+3x-2  =  (2x - 1) (x  + 2)

Uh-oh, Spawn......sounds like your schedule is rotten to the "core"....!!!!

Good, amazinggirl....how are you???

3% = .03

So

x = 5444.44/.03 =  $181,481.33

f(x) = 3x-7 and g(x) = -2x - 6. Find (f * g)(4)

[f * g](4)   means that we want to multipy these two functions together and then evaluate the resulting function for x = 4   ....so we have

[3x - 7] * [ -2x - 6]   =  -6x^2 + 14x -18x + 42  =   -6x^2 - 4x + 42

Now....replace the x's  with 4

-6*4^2 - 4(4)  + 42  =

-96 - 16 + 42  =

-70

Here's 2

lim x-->-∞ (x^1/3 - 5x + 3) / (2x + x^2/3 - 4)       divide each term by x

lim x-->-∞ ( x^1/3/x - 5x/x + 3/x) / (2x/x + x^2/3/x -4/x)

[ 0 -5  + 0]  / [2 + 0 -4]  =

-5/2

The ratio10:17  means that there are 27 "parts"   to his collection and the Blu-rays  comprise 10/27 of the total.......so....

10/27 * 837   =  310 Blu-rays

-2x+7>0     subtract 7 from each side

-2x  > -7    divide both sides by -2   and reverse the inequality sign

x < 7/2

6 + 2/3