Mid Term 1 (-->Section 2.6)

Question 1

sin^2 x + cos^2 x =

Answer 1

1

Question 2

piecewise definition of |X|

Answer 2

x if x>=0

-x if x<=0

Question 3

Even function

Answer 3

f(-x)=f(x)

symmetric over y=x

Question 4

Odd fcn

Answer 4

f(-x)=-f(x)

symmetric over y

Question 5

f(x) =x^a where a is a constant

Answer 5

power function

Question 6

rational function

Answer 6

ratio of polynomials

Question 7

domain of f-g fg or (f/g)

Answer 7

intersection of domains of f and g

g cannot be 0 for f/g

Question 8

f(x)=a^x where a is a constant

Answer 8

exponential fcn

Question 9

Domain of f(x)=a^x

Answer 9

all real numbers

Question 10

Range of f(x)=a^x

Answer 10

(0,infinity) for x != 1

(1) for x=1

Question 11

slope of e^x at (0,1)

Answer 11

1

Question 12

y intercept of e^x

Answer 12

1

Question 13

what does the inverse of a fcn look like

Answer 13

reflected over y=x

Question 14

when is x=a a vertical asymptote of f(x)

Answer 14

when lim(x–>a)f(x)= (+/-) infinity
Or
lim (x–a (+/-)) f(x) = (+/-) infinity

Question 15

as x–>a lim( f(x) + g(x) )

Answer 15

lim( f(x) ) + lim( g(x) ) if both limits exist

Question 16

as x–>a lim( f(x) - g(x) )

Answer 16

lim( f(x) ) - lim( g(x) ) if both limits exist

Question 17

as x–>a lim( c*g(x) )

Answer 17

c * lim( g(x) ) if limit g(x) exists

Question 18

as x–>a lim( f(x)g(x) )

Answer 18

(lim( f(x) ))(lim( g(x) ) if both limits exist

Question 19

as x–>a lim( f(x) / g(x) )

Answer 19

lim( f(x)) / (lim(g(x) ) if lim( g(x) ) != 0

Question 20

as x–>a lim( f(x) ^n)

Answer 20

(lim(f(x)))^n

Question 21

as x–>a limc

Answer 21

c

Question 22

as x–>a lim( x)

Answer 22

a

Question 23

Squeez Theorem

Answer 23

if f(x)<=h(x) and lim(x–a)(f(x))= lim(x–a)(h(x))=L then lim(x–a) exists and =L

Question 24

what does lim(x–>a)(f(x))= L mean

Answer 24

for any epsilon>0, there exists a delta >o s.t

0<epsilon

Question 25

what does the lim(x-->a) f(x) = infinity mean

Answer 25

for all M>0 there exists a delta>0 s.t 0M

Question 26

what does the lim(x-->a)f(x)= -infinity mean

Answer 26

for all N0 s.t 0

Question 27

When is a function cts at point a

Answer 27

when the fcn is defined at a and lim(x-->a)( f(x)) = f(a)

Question 28

Intermediate value theorem

Answer 28

if f is cts on a closed interval [a,b] let N be any number b/t f(g) and f(b) then there exists a number c that is in [a,b] s.t. f(c)=N

Question 29

definition of a limit at inifinity

Answer 29

if f is def on (a,infinity) (resp, (-infinity,a) then lim(x-->infinity) (f(x)) =L (resp, lim(x-->-infinity) (f(x)) =L)