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g(x) = x^2 - 5x (if <= -1)
ax^3 - 7 (if x > -1)
= 6
given the function f(x) = 4x^2 - x determine the equation of the tangent line at x = -1
-> y - 5 = -9(x + 1)
g(x) = x^2 - 3 (x < 1)
2x + 4 (x > 1)
lim x->1 g(x) = DNE
g(x) = x^2 - 5x (if x<= -1)
ax^3 - 7 (if x > -1)
determine "a" such that lim x -> -1 (g(x)) exists
= -13
find the limit of the function as x approaches 2+
= 5
the graph represents f(x)
find lim x->1
= DNE
evaluate the limit lim x->0 ((5x^4 + 8x^2)/(3x^4 - 16x^2))
= (x^2(5x^2+8))/(x^2(3x^2-16)) = (5x^2+8)/(3x^2-16)
find the limit of the function as x approaches 4 form the right
= 2
the figure shows the graph...which are true? I and II only
which of these statements about f(x) is true? 1. the function has a limit at x = 2 2. the function is continuous at x = 2
1 only
the graph represents f(x). find lim x->6 f(x)
= 5
the function f(x) is continuous over the interval [3, 8] and f(3) = -2 and f(8) = 5. check all of the following that must be true.
there is some value that f(x) = 3; ~~if "c" is on the interval [3,8]~~ WRONG BECAUSE IT CAN LEAVE THE RANGE
if f(x) = x^2 determine the value of lim x->0 (f(3+x) - f(3))/(x)
= (x+3)^2 - 9 x^2 + 6x + 9 - 9 x(x + 6)
------------------- = ----------------- = ----------- = x + 6 = 6 (somehow...oh wait because x is 0)
x x x
lim x -> 16 (sqrt(x) - 4))/(16 - x) CONJUGATE
sqrt(x) - 4 sqrt(x) + 4 x - 16 -1 -1
----------- X --------------- = ------------------- = ----------- = -------
16 - x sqrt(x) + 4 (16 - x)(sqrt(x) + 4) sqrt(x) + 4 8
evaluate the limit: lim x -> infinity (5x^3 + 2x - 1)/(2x^3 - 9)
= 5/2 (only highest degrees matter)
given the function f(x) = 4x^2 - x; determine the average rate of change over the interval [-1, 2]
simple slope ARC formula gives you = 3
14 - 5 9
------- = ---
2 - (-1) 3
given lim x -> infinity f(x) = -2; which of the following statements must be true?
f(0) = -2
= none of the above
evaluate the limit: lim x->1 (7x-18)/((x-2)^2)
= -11
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