# Calculus

posted by .

Find the constant c so that
lim [x^2 + x + c]/[x^2 - 5x + 6] exists.
x->3

For that value of c, determine the limit. (Hint: Find the value of c for which x - 3 is a factor of the numerator.)

• Calculus -

factor the bottom
(x-3)(x-2)

factor the top with (x-3) a factor so we can cancel it
(x-3)(x+b) = x^2+x+c
x^2 - 3x +b x - 3 b = x^2 + x + c
so
b x -3 x = x so b = 4
then c = -12
so
(x^2 + x - 12)/(x^2 - 5 x + 6)

(x-3)(x+4) / [(x-3)(x-2)]

(x+4)/(x-2)
when x = 3
7/1 = 7

• Calculus -

hmmm. looks familiar. Anyway,

denominator is (x-3)(x-2), so we want the top to be
(x-3)(x-k) so that the fraction exists everywhere except at x=3, but has a finite limit there.

x^2 - (k+3)x + 3k = x^2 + x + c
k+3 = -1
k = -4

so c = 3k = -12

x^2 + x + c = x^2 + x -12 = (x-3)(x+4)

## Similar Questions

1. ### CALCULUS - need help!

Determine the limit of the trigonometric function (if it exists). 1. lim sin x / 5x (x -> 0) 2. lim tan^2x / x (x ->0) 3. lim cos x tan x / x (x -> 0)
2. ### Calculus

Find a value of the constant k such that the limit exists. lim x->1 (x^2-kx+4)/(x-1) Is the answer 5?
3. ### Calculus

Find the positive integers k for which lim ->0 sin(sin(x))/x^k exists, and then find the value the limit. (hint:consider first k=0, then k=1. Find the limit in these simple cases. Next take k=2 and finally consder k>2 and find …
4. ### Calculus

is there a number a such that the lim x->2 6x^2+ax+a+57/x^+x-6 exists?
5. ### Calculus

If f(x) = { √2-x x < 2 { x^3 + k(x+1) x ≥ 2 determine the value of the constant k for which lim exists. x->2
6. ### Calculus 3

Find the limit, if it exists, or show that the limit does not exist. lim of x+y/y^2-x^2 as (x,y) approaches the point (-1,1).
7. ### Calculus 3

Find the limit, if it exists, or show that the limit does not exist. lim of x+y/y^2-x^2 as (x,y) approaches the point (-1,1).
8. ### calculus

(a) Find the number c such that the limit below exists. Limit as x goes to -2 of: x^2+cx=c-3/x^2+2x (b) Calculate the limit for the value of c in part (a).
9. ### Calculus

Find a value of the constant k such that the limit exists. x^2-k^2 lim _________ x->8 x-8 k=+/_
10. ### Math (Calculus - Limits)

Find the constant c so that lim x->8 x^2+2x+c/x^2-15x+56 exists. For that value of c, determine the limit. (Hint: Find the value of c for which x-8 is a factor of the numerator). I understand that I should set (x-8)(x+b) equal to …

More Similar Questions