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1. What is the slope of the line y = x2 + x + 2 through (−1, 2) and (x, y) when:
a) x = −1 + h?
b) What happens to this last slope when h is very small (close to 0)?
2. For f (x) = x^2− x − 6 and g(x) = x^2− 2x − 3, evaluate:
a) lim〖[f(x)+g(x)]〗 b) lim〖f(x)*g(x)〗 c) lim〖f(x)*g(x)〗
x→1 x→1 x→3
d) lim〖f(x)/g(x)〗 e) lim〖〖f(x)〗^3 〗
x→1 x→1
3. Knowing that lim 5x − 3 = 2, what values of x guarantee that f (x) = 5x − 3 is within :
x→1
a) 1 unit of 2? b) 0.5 units of 2?
4. Approximate the value of each of the following limits:
5. x and y are integers
x + y < 11 , and x > 6
What is the smallest possible value of x - y ?
For the next problems use the next Limit Properties:
Suppose lim(x + c) f(x) and lim(x + c) g(x) both exist. The following then are true:
lim [f(x) + g(x)] = limf(x) + limg(x)
lim [f(x) - g(x)] = limf(x) - limg(x)
lim [f(x)* g(x)] = limf(x) * limg(x)
lim [f(x)/ g(x)] = lim f(x) / lim g(x) lim g(x) ≠0
lim [r *f(x)= r* lim f(x) for any constant r
lim r = r
lim 〖[f(x)]〗^n=[limf(x)]^n
lim√(n&f(x))= √(n&limf(x))
6. Use the Limit Properties to find the following limits, if they exist.
a)lim┬(x→3)〖(4〗〖x^3-2〗 x^2+7x+5) b)lim┬(x→-1)〖(2x^3-3x^2+x-1)/(1-x^3 )〗 c) lim┬(x→1)∛(x^4-3x^2+2x+1)
7. Use the Limit Principles to find the following limits:
a)lim┬(x→2)√(2&(x^2-4)/(x-2)) b) lim┬(x→2)〖((x^2-4)/(x-2))^2 〗 c) lim┬(x→2)10
8. For the functions functiile f : R →R, f(x) = x - 1 and g: R → R, g(x) = 3x + 1 calculate:
a) f ○ f ; f○ g, g ○ f, g ○ g ; b) f ○f○f; f of o g; fog f; gog og .
9. What is the domain and range of each of the following functions?
a) y = 3sin(2x) b) y = (x^2-9)/(x-3)
10. Consider the function f(x)=(2/x^2 +3x)/(1/x+1/x^2 ) defined for x≠1,0
Which is the lim f(x) when x→0.

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