Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
26.do no 1 only do like example 4 given
![Use implicit differentiation to find the gradient of the tangent to the curve
nd the equation of the tangent line to the curve
ind the equation of the tangent line to the curve x xy + 3y =
26 TANGENT LINE AND IMPLICIT DIFFERENTIATION
Find the equation of the tangent line to the curve xy = 4 + In x at the point (1
MAT 42
TUTORIAL 26
6 at Q(-1,2).
2.
* * xy - y = 1 at the point (2, 3).
3.
sin xy = y at (, 1).
at the gradient of the tangent to the curve v (x + 2) + tan 2x - 8 = 0
the point (0,2).
Use implicit differentiation to find the gradient of the tangent line for
x'y
6xy
- 2x = 9 at the point (-1, 1).
Use implicit differentiation to find the gradient of the tangent line for
+ 2 sin x = 4y at the point (n, 2).
y
dy
dx
Hence, find the equation of the tangent line to the curve 6 + sin 2y :
Find
if 6 + sin 2y =
2y°
+ 3x by using implicit differentiation.
2y + 3x
%3D
at the point (2,0).
lee implicit differentiation to find the equation of the tangent line to the curve
+ sin x = 2y at the point (t, 2).
the point ( 1, 2).
at
f the tangent](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F094a68cb-ae8f-4a26-8f61-869c6519ee11%2Ff34483bf-d383-4ea8-845f-9342be38d08d%2Fn0u2oi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use implicit differentiation to find the gradient of the tangent to the curve
nd the equation of the tangent line to the curve
ind the equation of the tangent line to the curve x xy + 3y =
26 TANGENT LINE AND IMPLICIT DIFFERENTIATION
Find the equation of the tangent line to the curve xy = 4 + In x at the point (1
MAT 42
TUTORIAL 26
6 at Q(-1,2).
2.
* * xy - y = 1 at the point (2, 3).
3.
sin xy = y at (, 1).
at the gradient of the tangent to the curve v (x + 2) + tan 2x - 8 = 0
the point (0,2).
Use implicit differentiation to find the gradient of the tangent line for
x'y
6xy
- 2x = 9 at the point (-1, 1).
Use implicit differentiation to find the gradient of the tangent line for
+ 2 sin x = 4y at the point (n, 2).
y
dy
dx
Hence, find the equation of the tangent line to the curve 6 + sin 2y :
Find
if 6 + sin 2y =
2y°
+ 3x by using implicit differentiation.
2y + 3x
%3D
at the point (2,0).
lee implicit differentiation to find the equation of the tangent line to the curve
+ sin x = 2y at the point (t, 2).
the point ( 1, 2).
at
f the tangent
![Find the slope of the tangent to the curve y+ sin x = 4y at the point (t, 2).
26 TANGENT LINE AND IMPLICIT DIFFERENTIATION
TANGENT LINE AND IMPLICIT DIFFERENTIATIO
Example 4:
Solution:
+ sin x
4y
%3D
dy
dy
3y2
dx
+ cos x =
At (, 2 ); 3 (2 )
dy
+ COS T
dx
dy
4
dx
%3D
dy
dx
dy
4.
dx
12
- 1 =
1
dx
dy
dx
%3D
ample 5:
- implicit differentiation to find the equation of the tangent line to the curve
- 2x = (y - 1)° + 4 cos y at y = 0.
ution:
exy - 2x
(y - 1)° + 4 cos y
e° - 2x
(-1)° + 4 cos 0
- 1 + 4
- 2
= 0,
%3D
1
- 2x
2x
!!
%3D
- 1
2.
5 ( v
1a dy
dv
1/8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F094a68cb-ae8f-4a26-8f61-869c6519ee11%2Ff34483bf-d383-4ea8-845f-9342be38d08d%2Fm22sq89_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the slope of the tangent to the curve y+ sin x = 4y at the point (t, 2).
26 TANGENT LINE AND IMPLICIT DIFFERENTIATION
TANGENT LINE AND IMPLICIT DIFFERENTIATIO
Example 4:
Solution:
+ sin x
4y
%3D
dy
dy
3y2
dx
+ cos x =
At (, 2 ); 3 (2 )
dy
+ COS T
dx
dy
4
dx
%3D
dy
dx
dy
4.
dx
12
- 1 =
1
dx
dy
dx
%3D
ample 5:
- implicit differentiation to find the equation of the tangent line to the curve
- 2x = (y - 1)° + 4 cos y at y = 0.
ution:
exy - 2x
(y - 1)° + 4 cos y
e° - 2x
(-1)° + 4 cos 0
- 1 + 4
- 2
= 0,
%3D
1
- 2x
2x
!!
%3D
- 1
2.
5 ( v
1a dy
dv
1/8
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