Calculus Question Bank 2024

Calculus Question Bank




University of New South Wales

Math 1231

, calculus QB-1 sixparxxB xx *******885)(x,y):(-1,2) 0.0cm




1) f(x,y) x2 6y
=
+
z 2
=
82 3
-




x +6y 0 ofz:
possible error
=




max

64 =
- x2

y = -



1
0z =




22.0x 2oz.dy +




i-ey -- I see the graphthatare
when:
0z=12.0.011 1-3.001/ +




Ot =
0.01 + 0.03

Oz = 0.05




1tili
2) z (2x
=
-

y 3)
+
-
1 and When 2x<y


When:z 2
=
3 =
-
(2x -

y +

3) 6) z = -
x3 -

4ySit 7
=




2 (2x
= -

y +
31 -
1 3 = -
2x y + -
3
x 1
=
y =.c d =
-

1
1D
dt
-
=
2



6 2x +y
find:at t=
=




when
- =




When 2xiy

3 (2x= -

y 3/
+
y 2x 6
= +



↳ 1(z) =?
0 2x

zdz.dT dta
=
-
y

y 2x
=




ly2.
tili y <- answer
=
-3x2.dX -




= -
3(1)". -
1 -
12 - 2)2.1 2) -




& -

·

=3 96



:
+




i 1
z 99
=




X
-

1 2



7) z =
- x2 -
4y3
Pl0t:
dy=
2
3) f(x,y) f(y,X) =
put random
numbers
g(X,y) g(x, =
-

y) d4 = e
+
3


f(0,1) f(1.0) =
/
g(1,1) 9(1, -1)
= X =
1
-
y = -
1



1) When t = 0




Y 4
=

+ 0 4 1
=
+
5
=




·) d. Az AYdtda
h(x, y) h(0,y)
=

k(X,y) k(X,0) =

=
-
2( 1).5 1
- +
-
12 -
1)2)(3)


u(2,1) h
= (0,1) K (5,5):K (5,0) 10
=
-

36
other eg:

Az = -
26
y(siny7) 7.y6.cos(y)),/ =




·
8) F x(y =
-

3x-y -
5xyz 7x+y7
+




snly-5) 7a
+
*




+F. .
4) f(x,y) f(-y, x) try with numbers (X3 3x3 10X8 49x +y6
cosly"))
-

-
=


+
- - -
+




X y 0X -y
+
= = - -
x 0
=




=)
y x =
- = 3x2 -
6x -

187 343x6y6
+