Question

Linear approximation tan(44)

Answer 1

tan(45-1)

Answer 2

f(x) = tan x

Answer 3

yep

Answer 4

f'(x)=sec^2(x)

Answer 5

f(a)-f'(a)(x-a)

Answer 6

tan45=1

Answer 7

sec^2(45)=2

Answer 8

yup, you are going good.

Answer 9

\[1+2(x-a)\]

Answer 10

this is where im stuck

Answer 11

a=45?

Answer 12

x=44?

Answer 13

you took a= 45, thats correct,
take x= 1

Answer 14

-1 degrees?

Answer 15

what is in the left side of f(a)-f'(a)(x-a) ??

Answer 16

f(a) = tan45

Answer 17

f'(a)=sec^2(45)

Answer 18

x=44 degrees?

Answer 19

i meant its f(x-a) = f(a)-f'(a)(x-a)
right?
a=45 is correct

Answer 20

take x=1

Answer 21

ok so, 1-45?

Answer 22

-44 degrees?

Answer 23

and tan(-y)=-tan y

Answer 24

its actually f(x)= f(a) +f'(a) (x-a)

Answer 25

i hate the x-a part

Answer 26

the statement is true for x in the *neighborhood* of a
remember that f(a) is the value that is easy to find, and f(x) is the value that we are going to find at the end

Answer 27

f(a) + f'(a)(x-a) ......a=45, x=44

=1 + 2*tan(44 - 45)

Answer 28

tan(-1degrees)

Answer 29

yup, its -0.017

Answer 30

==1 + 2*tan(44 - 45)
=1 + 2( -0.017)
= 1 - 0.034
=?

Answer 31

.968

Answer 32

if the book has .965, thats close enough?

Answer 33

1-0.034 = 0.966
this is close enough

Answer 34

also, am I supposed to use a calc to find tan-1

Answer 35

i don't see any other way out.
for more accuracy, tan(-1)=-0.174
then tan 44=0.965

Answer 36

ahhh, ok, that clears it all up for me, i just need to remember to place tan(x-a) thanks @hartnn !!!!!!

Answer 37

welcome ^_^

Answer 38

(^^^)

Answer 39

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