Estimate Δf using the Linear Approximation and use a calculator to compute the error.
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Estimate Δf using the Linear Approximation and use a calculator to compute the error.
$f(x)= sqrt3+x$
$a=6$
$Δx= 0.5$
$Δf approx frac112$
^ I got this part, just take the derivative.
With these calculations, we have determined that the square root of _____
^I was thinking it was the $sqrt9$, but that is incorrect
is approximately _____
^obviously thought this was $3$
The error in Linear Approximation is: _____
^Went through the whole process of trying to find the approximation, ended up with a $negative$ number though $-107.38%$
[Note: This is not asking for relative error or percent error.]
My main struggle is trying to understand what they are asking for?
Any ideas?
calculus
edited Mar 30 '16 at 4:25
user21820
35.9k440138
asked Mar 30 '16 at 4:17
pewpew
7117
 |Â
show 4 more comments
up vote
0
down vote
favorite
Estimate Δf using the Linear Approximation and use a calculator to compute the error.
$f(x)= sqrt3+x$
$a=6$
$Δx= 0.5$
$Δf approx frac112$
^ I got this part, just take the derivative.
With these calculations, we have determined that the square root of _____
^I was thinking it was the $sqrt9$, but that is incorrect
is approximately _____
^obviously thought this was $3$
The error in Linear Approximation is: _____
^Went through the whole process of trying to find the approximation, ended up with a $negative$ number though $-107.38%$
[Note: This is not asking for relative error or percent error.]
My main struggle is trying to understand what they are asking for?
Any ideas?
calculus
edited Mar 30 '16 at 4:25
user21820
35.9k440138
asked Mar 30 '16 at 4:17
pewpew
7117
I've no idea what your first few lines mean.
– user21820
Mar 30 '16 at 4:27
I was hoping I wasn't the only one.
– pewpew
Mar 30 '16 at 4:28
Are you sure the question states exactly that? What is $a$?
– user21820
Mar 30 '16 at 4:31
Maybe you're supposed to find $sqrt9.5 using linear approximation and then determine the error.
– Neal
Mar 30 '16 at 4:32
@Neal: That's what I would guess also.
– user21820
Mar 30 '16 at 4:33
 |Â
show 4 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Estimate Δf using the Linear Approximation and use a calculator to compute the error.
$f(x)= sqrt3+x$
$a=6$
$Δx= 0.5$
$Δf approx frac112$
^ I got this part, just take the derivative.
With these calculations, we have determined that the square root of _____
^I was thinking it was the $sqrt9$, but that is incorrect
is approximately _____
^obviously thought this was $3$
The error in Linear Approximation is: _____
^Went through the whole process of trying to find the approximation, ended up with a $negative$ number though $-107.38%$
[Note: This is not asking for relative error or percent error.]
My main struggle is trying to understand what they are asking for?
Any ideas?
calculus
edited Mar 30 '16 at 4:25
user21820
35.9k440138
asked Mar 30 '16 at 4:17
pewpew
7117
Estimate Δf using the Linear Approximation and use a calculator to compute the error.
$f(x)= sqrt3+x$
$a=6$
$Δx= 0.5$
$Δf approx frac112$
^ I got this part, just take the derivative.
With these calculations, we have determined that the square root of _____
^I was thinking it was the $sqrt9$, but that is incorrect
is approximately _____
^obviously thought this was $3$
The error in Linear Approximation is: _____
^Went through the whole process of trying to find the approximation, ended up with a $negative$ number though $-107.38%$
[Note: This is not asking for relative error or percent error.]
My main struggle is trying to understand what they are asking for?
Any ideas?
calculus
edited Mar 30 '16 at 4:25
user21820
35.9k440138
asked Mar 30 '16 at 4:17
pewpew
7117
edited Mar 30 '16 at 4:25
user21820
35.9k440138
edited Mar 30 '16 at 4:25
user21820
35.9k440138
edited Mar 30 '16 at 4:25
user21820
35.9k440138
35.9k440138
asked Mar 30 '16 at 4:17
pewpew
7117
asked Mar 30 '16 at 4:17
pewpew
7117
asked Mar 30 '16 at 4:17
pewpew
7117
7117
I've no idea what your first few lines mean.
– user21820
Mar 30 '16 at 4:27
I was hoping I wasn't the only one.
– pewpew
Mar 30 '16 at 4:28
Are you sure the question states exactly that? What is $a$?
– user21820
Mar 30 '16 at 4:31
Maybe you're supposed to find $sqrt9.5 using linear approximation and then determine the error.
– Neal
Mar 30 '16 at 4:32
@Neal: That's what I would guess also.
– user21820
Mar 30 '16 at 4:33
 |Â
show 4 more comments
I've no idea what your first few lines mean.
– user21820
Mar 30 '16 at 4:27
I was hoping I wasn't the only one.
– pewpew
Mar 30 '16 at 4:28
Are you sure the question states exactly that? What is $a$?
– user21820
Mar 30 '16 at 4:31
Maybe you're supposed to find $sqrt9.5 using linear approximation and then determine the error.
– Neal
Mar 30 '16 at 4:32
@Neal: That's what I would guess also.
– user21820
Mar 30 '16 at 4:33
I've no idea what your first few lines mean.
– user21820
Mar 30 '16 at 4:27
I've no idea what your first few lines mean.
– user21820
Mar 30 '16 at 4:27
I was hoping I wasn't the only one.
– pewpew
Mar 30 '16 at 4:28
I was hoping I wasn't the only one.
– pewpew
Mar 30 '16 at 4:28
Are you sure the question states exactly that? What is $a$?
– user21820
Mar 30 '16 at 4:31
Are you sure the question states exactly that? What is $a$?
– user21820
Mar 30 '16 at 4:31
Maybe you're supposed to find $sqrt9.5 using linear approximation and then determine the error.
– Neal
Mar 30 '16 at 4:32
Maybe you're supposed to find $sqrt9.5 using linear approximation and then determine the error.
– Neal
Mar 30 '16 at 4:32
@Neal: That's what I would guess also.
– user21820
Mar 30 '16 at 4:33
@Neal: That's what I would guess also.
– user21820
Mar 30 '16 at 4:33
 |Â
show 4 more comments
1 Answer
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$$quadf(X+Delta x) sim f(x) +Delta x .f'(x)\f(x)=sqrt3+x,f'(x)=frac12sqrt3+x\to\f(6+.5)sim f(6) +.5 frac12sqrt9=3+0.5*frac16=3+frac112$$now $$f(6+Delta x)-f(6)sim frac112=0.083333333...$$
without approximation $$sqrt3+6+0.5-sqrt3+6=0.0822070014844...$$
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
$$quadf(X+Delta x) sim f(x) +Delta x .f'(x)\f(x)=sqrt3+x,f'(x)=frac12sqrt3+x\to\f(6+.5)sim f(6) +.5 frac12sqrt9=3+0.5*frac16=3+frac112$$now $$f(6+Delta x)-f(6)sim frac112=0.083333333...$$
without approximation $$sqrt3+6+0.5-sqrt3+6=0.0822070014844...$$
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
add a comment |Â
up vote
0
down vote
$$quadf(X+Delta x) sim f(x) +Delta x .f'(x)\f(x)=sqrt3+x,f'(x)=frac12sqrt3+x\to\f(6+.5)sim f(6) +.5 frac12sqrt9=3+0.5*frac16=3+frac112$$now $$f(6+Delta x)-f(6)sim frac112=0.083333333...$$
without approximation $$sqrt3+6+0.5-sqrt3+6=0.0822070014844...$$
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
add a comment |Â
up vote
0
down vote
up vote
0
down vote
$$quadf(X+Delta x) sim f(x) +Delta x .f'(x)\f(x)=sqrt3+x,f'(x)=frac12sqrt3+x\to\f(6+.5)sim f(6) +.5 frac12sqrt9=3+0.5*frac16=3+frac112$$now $$f(6+Delta x)-f(6)sim frac112=0.083333333...$$
without approximation $$sqrt3+6+0.5-sqrt3+6=0.0822070014844...$$
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
$$quadf(X+Delta x) sim f(x) +Delta x .f'(x)\f(x)=sqrt3+x,f'(x)=frac12sqrt3+x\to\f(6+.5)sim f(6) +.5 frac12sqrt9=3+0.5*frac16=3+frac112$$now $$f(6+Delta x)-f(6)sim frac112=0.083333333...$$
without approximation $$sqrt3+6+0.5-sqrt3+6=0.0822070014844...$$
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
edited Jul 11 at 21:18
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
answered Mar 30 '16 at 4:44
Khosrotash
16.7k12159
16.7k12159
add a comment |Â
add a comment |Â
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I've no idea what your first few lines mean.
– user21820
Mar 30 '16 at 4:27
I was hoping I wasn't the only one.
– pewpew
Mar 30 '16 at 4:28
Are you sure the question states exactly that? What is $a$?
– user21820
Mar 30 '16 at 4:31
Maybe you're supposed to find $sqrt9.5 using linear approximation and then determine the error.
– Neal
Mar 30 '16 at 4:32
@Neal: That's what I would guess also.
– user21820
Mar 30 '16 at 4:33