Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Except #1 (b)
![1. Evaluate the following limits.
(a)
Let
2.
3.
(b)
(c)
a- - 3r
p(x)=ar +36
4r+b
where a and b are constants. Find a and b so that lim f(x) and lim f(z) both exists.
1+√k+K²+1
lim
24³ +3
Use the definition of limit of a function to prove that lim f(x) = -6 if
if x < -2
if -2<r<1
ifr>1
f(x) =
Find all values of a such that
is continuous everywhere.
16²-9 if x-
4x+3
if r = -1.
fr+2 ifr <a
B(x) =
if z > a
Prove that p(7)=¹77² +7+4 has at least two real zeros.
Let / be a continuous on the interval [0, 1] to R and such that f(0) = ((1). Show that there
exists a point a in [0,1/2] such that ((a) = l(a + 1/2).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd692ddcb-0acb-471d-af7c-290dbafe10ae%2Fc562676c-1246-4dc6-9940-0f098add218d%2Ftca1hnm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Evaluate the following limits.
(a)
Let
2.
3.
(b)
(c)
a- - 3r
p(x)=ar +36
4r+b
where a and b are constants. Find a and b so that lim f(x) and lim f(z) both exists.
1+√k+K²+1
lim
24³ +3
Use the definition of limit of a function to prove that lim f(x) = -6 if
if x < -2
if -2<r<1
ifr>1
f(x) =
Find all values of a such that
is continuous everywhere.
16²-9 if x-
4x+3
if r = -1.
fr+2 ifr <a
B(x) =
if z > a
Prove that p(7)=¹77² +7+4 has at least two real zeros.
Let / be a continuous on the interval [0, 1] to R and such that f(0) = ((1). Show that there
exists a point a in [0,1/2] such that ((a) = l(a + 1/2).
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