Find a lim 2 3x25x2 4x x Infinity b lim x sqrtx2 2x x i

Find:

a)

lim: ( 2 - 3x^2)/(5x^2 + 4x)

x-> Infinity

b)

lim: (x + sqrt[x^2 + 2x])

x-> -infinity

c)

Sketch the graph of one function that does all the following.

lim f(x) = -infinity

x-> 3

lim f(x) = 2

x-> infinity

f(0) = 0 , f is even.

Solution

divide by x*X both in numerator and denomiantor

: 2/x*X - 3 / 5 + 4/x

: -3/5

b) infinity + infinity = infinity

c) f(x) = -1/(x-3) + 1/(x-2) + 1/6