1. ## Limits

1. )Let f(x)=3 ·x^9 -10 ·x^3 +2 and g(x)=c·x^n -7 ·x^3 +18 with c cannot = 0. Then

lim (-->infinite) f(x)/g(x)= infinite

c (>, < or =) to ________ and n (>, < or =) to ________ .

2.)The function

f(x)= -4·x^2+4 if x >(and equal to) -2
d-x if x -2

is continuous at x=-2 if and only if d = _______________

3.) The set of all points of discontinuity of the function

g(x)= x+4 / x^2-16

equals
a) {4}
b) {4,-4 }
c) {-4 }

sorry..hope you understand the notations...

2. sorry, can't understand your post..

3. sorry..i edited it..hope you understand it now

4. Hello,

1. )Let f(x)=3 ·x^9 -10 ·x^3 +2 and g(x)=c·x^n -7 ·x^3 +18 with c cannot = 0. Then

lim (-->infinite) f(x)/g(x)= infinite

c (>, < or =) to ________ and n (>, < or =) to ________ .
$\displaystyle Polynomial=a_n x^n+a_{n-1} x^{n-1}+\dots+a_1 x+a_0$

$\displaystyle a_n \neq 0$

$\displaystyle a_n$ is the leading coefficient.
$\displaystyle n$ is the degree of the polynomial.

The limit of the quotient of two polynomials is :

- infinity if the degree of the polynomial above is superior to the degree of the polynomial below. The sign of it depends on the leading coefficient.
- the quotient of the leading coefficients if the leading coefficients above and below are the same.
- 0 if the degree of the polynomial below is superior to the degree of the polynomial above.

2.)The function

f(x)= -4·x^2+4 if x >(and equal to) -2
d-x if x -2

is continuous at x=-2 if and only if d = _______________
For this to be continuous, you must have :

$\displaystyle \lim_{x \to 2^-} f(x)= \lim_{x \to 2^+} f(x)$

$\displaystyle \Longleftrightarrow \lim_{x \to 2} \ d-x=\lim_{x \to 2} \ -4x^2+4$

Just replace and find the value of d

3.) The set of all points of discontinuity of the function

g(x)= x+4 / x^2-16

equals
a) {4}
b) {4,-4 }
c) {-4 }
Change the denominator into $\displaystyle x^2-16=(x-4)(x+4)$.
Simplify, and then conclude

5. i don't get the 2nd question...how do i replace and find the value of d?...