CPhill

3x^2+14x+8   =

(3x + 2) (x + 4)

I assume that the first one is :

lim x → −∞ 4e^x = 0

Note that, as x  → −∞, e^x will grow smaller and smaller.....and if we let x assume some large negative value, e^x, will approach 0

Therefore,

lim x → −∞ 4e^x = 0

Likewise, I assume that the second one is :

lim x → ∞ 2e^x = ∞

Again, if we let x approach some large positive value, e^x will grow larger and larger. So, as x → ∞ , e^x  will also approach ∞

Here's the graph of e^x that will give you some idea of the end behaviors of both functions :

https://www.desmos.com/calculator/ml0aj0en2z

Just hit the "2nd"  button.......you will see "atan"   [tangent inverse ]

Here you go :   http://www.wolframalpha.com/input/?i=.11^300

12 x  $560  = $6720  (less)

On the calculator, DS  type :

Sum(a,d)

You will see....

Pretty funny, U101....been here almost 2 years and never discovered that....!!!!

Here's some, U101......http://www.archtoolbox.com/representation/abbreviations/electabbrev.html

(mg⁴)^-1(m¹g⁴)  =

(m^-1g^-4)(m¹g⁴)  =

(m⁰g⁰)  =

(mg)⁰  =

1

sqrt(400^2 + 1050^2)  = about 1123.6 ft