AMMAT2A/AMMAA2A
TOTAL MARKS: 50
CASS 1
MARKED OVER: 50
24 AUGUST 2023
DURATION: 90 min.
Instructions: Answer all questions. You may start with any question and make sure that your questions
numbering is correct. Where decimals results, leave your answer in three decimal places.
1. Find the following derivatives
1.1.
y = cos-1
1.2.
y = In (coshx-1).
1.3.
y = tanh-1 (122).
dy
d2y
dx
dx2
[9]
[9]
[9]
[5]
2. Find and of the parametric equation x = cose + Osine and y = sine - @cose.
3. Find the coordinates of P that maximize the area of the rectangle shown in the figure below. P is a point at
the corner of the rectangle along a straight line passing through (0,3) and (4,0).
[9]
(0,3)
4. Given the function f(x, y) = xln(x² + y). Find fx, fy and fxy.
FORMULA SHEET
(4,0)
x
TABLE OF DERIVATIVES
Inverse Trigonometric Functions
Inverse Hyperbolic Functions
d
f'(x)
d
f'(x)
-1
(sin¯¹ f(x)) =
(sinh¯¹ f(x)) =
dx
d
a2 - [f(x)]2
-f'(x)
dx
d
√1 + [f(x)]2
f'(x)
(cos-¹ f(x)) =
dx
d
√a²- [f(x)]2
f'(x)
dx (cosh-¹ f(x))
=
√[f(x)]2-1
d
f'(x)
(tan-¹ f(x)) =
1 + [f(x)]2
dx (tanh-¹ f(x)) = 1 - [f(x)]2
[9]
[50]
