MATH 1252 Arizona State University Mathematics Problems Hi i need your help in this assignment just check the file that i attachment i want you to do the a

MATH 1252 Arizona State University Mathematics Problems Hi i need your help in this assignment just check the file that i attachment i want you to do the answer in word file MATH1252 Homework 2
Due Wednesday 7/15
1. Let limx?4 f (x) = 8 and limx?4 g(x) = 27. Use the limit rules to find each
limit.
(a) limx?4 log2 f (x)
(b) limx?4 [1 + f (x)]2
(c) limx?4
5g(x)+2
1?f (x)
2. Determine whether each limit exists. If yes, find its value.
x2 ?3x?10
x?5
8x+2
limx?? 4x?3
(a) limx?5
(b)
(c) limx??
5×2 +1
2×3 ?1
3. Let G(x) =
?6
(x?4)2
(a) Find limx?4 G(x).
(b) find the vertical asymptote of the graph of G(x).
(c) Compare your answers for parts (a) and (b). Are they related? How?
4. Find all values x = a where the function is discontinuous. For each value of
x, either find the limit of the function as x approaches a, or note when the
limit doesn’t exist.
(a) f (x) =
(b) r(x) =
(c) j(x) =
?2x
(2x+1)(3x+6)
|5?x|
x?5
ln | x+1
|
x?2
5. For the given piecewise function, find all values of x where the function is
discontinuous.
?
?
if x < 0 ?0 2 (a) f (x) = x ? 5x if 0 ? x ? 5 ? ? 5 if x > 5
(
x2 + x ? 12 if x ? 1
(b) g(x) =
3?x
if x > 1
6. Find the average rate of change for each function over the given interval.
(a) y = ?4×2 ? 6 between x = 1 and x = 3
(b) y =
?
3x ? 2 between x = 1 and x = 2
7. Find the instantaneous rate of change for each function at the given value.
(a) s(t) = ?4t2 ? 6 at t = 2
(b) F (x) = x2 + 2 at x = 0
8. Using the definition of the derivative, find f 0 (x).
(a) f (x) = 6×2 ? 5x ? 1
(b) f (x) = 4×3 ? 3
9. For each function, find (a) the equation of the secant line through the points
where x has the given values, and (b) the equation of the tangent line when
x has the first value.
(a) f (x) = 6 ? x2 ; x = ?1, x = 3
(b) f (x) =
?3
;
x+1
x = 1, x = 5

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