QI/ Answer two only A) Determine the equation of the tangent line to the curve xsin(y) – x'cos(y) = 1 at the point (1,4) B) Find the equations of all lines having slope -1 that are tangent to the curve y (x-3) C) Find the equation of tangent to the curve 4x²+ 9y² = 36 at the point (3 cos 0, 2 sin 0). %3D

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 45E
icon
Related questions
Question
100%
QI/
Answer two only
A) Determine the equation of the tangent line to the curve xsin(y) – x²cos(y) = 1 at the point
(1,)
B) Find the equations of all lines having slope -1 that are tangent to the curve y =
(х-3)
C) Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos 0, 2 sin 0).
Transcribed Image Text:QI/ Answer two only A) Determine the equation of the tangent line to the curve xsin(y) – x²cos(y) = 1 at the point (1,) B) Find the equations of all lines having slope -1 that are tangent to the curve y = (х-3) C) Find the equation of tangent to the curve 4x² + 9y² = 36 at the point (3 cos 0, 2 sin 0).
v'):-
Q3/ A)Find the following derivatives
1+5t
2)
y = 10V – Vz7 + 6V – 3
%3D
In(t)
3)y = (5x³ – 3)5 V-4x5 – 3
4) e2x+3y = x? – In(xy³)
sin(x)
В) If у %3D
find y', y",y'"' ?
Q4) Prove each of the following:
1+sinx
(2) [tanh (sinx)]:
cos x
(1)
1+sinx
= 2secx
= secx
cos x
(3) (xlnx) = -
1+sinx
(4)tan²x + 1 + tanxsecx =
dx3
cos'x
Transcribed Image Text:v'):- Q3/ A)Find the following derivatives 1+5t 2) y = 10V – Vz7 + 6V – 3 %3D In(t) 3)y = (5x³ – 3)5 V-4x5 – 3 4) e2x+3y = x? – In(xy³) sin(x) В) If у %3D find y', y",y'"' ? Q4) Prove each of the following: 1+sinx (2) [tanh (sinx)]: cos x (1) 1+sinx = 2secx = secx cos x (3) (xlnx) = - 1+sinx (4)tan²x + 1 + tanxsecx = dx3 cos'x
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Knowledge Booster
Implicit Differentiation
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781305652224
Author:
Charles P. McKeague, Mark D. Turner
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning