MATHEMATICS ASSIGNMENT
1.1 Find equations of the tangent line to the curve 𝑦 = 𝑥 + 2𝑥 − 𝑥 at the point (1; 2)
1.2 The equation of motion of a particle is 𝑠 = 𝑡 − 2𝑡 + 𝑡 − 𝑡, where s is in metres
and t is in seconds.
a) Find the velocity and acceleration as functions of t
b) Find the acceleration after 1 s
Differentiate the function and simplify the answer:
2.1 𝑓 (𝑥 ) =
–
2.2 ℎ (𝑥 ) =
Differentiate: 3.1 𝑦=𝑒 cos 4𝑡
3.2 𝑦 = tan(sin 𝑥)
–
3.3 𝑦 = 10
Find by implicit differentiation: 4.1 𝑥𝑒 = 𝑥 − 𝑦
4.2 4 cos 𝑥 sin 𝑦 = 1
5.1 Find the derivative of 𝑦 = tan √𝑥 in terms of x
5.2 Differentiate: a) ℎ(𝑥) = √𝑥
b) 𝑔(𝑥 ) = ln(sec 𝑥 + tan 𝑥)
, ANSWERS
1.1 𝑦 = 𝑥 + 2𝑥 − 𝑥 and the point (1; 2)
𝑦 = 4𝑥 + 4𝑥 − 1
𝑚 =7
Equation of tangent at (1; 2):
𝑦 − 2 = 7(𝑥 − 1)
𝑦 = 7𝑥 − 5
1.2
a) 𝑣 = 4𝑡 − 6𝑡 + 2𝑡 − 1
𝑎 = 12𝑡 − 12𝑡 + 2
b) 𝑎 = 2 𝑚. 𝑠
2.1 𝑓(𝑥) =
( ) ( )
𝑓 (𝑥) =
( )
=
( )
=
( )
=
2.1 ℎ(𝑥) =
( ) ( )
ℎ (𝑥) =
=
=
=
= cos 𝑥 + sin 𝑥
1.1 Find equations of the tangent line to the curve 𝑦 = 𝑥 + 2𝑥 − 𝑥 at the point (1; 2)
1.2 The equation of motion of a particle is 𝑠 = 𝑡 − 2𝑡 + 𝑡 − 𝑡, where s is in metres
and t is in seconds.
a) Find the velocity and acceleration as functions of t
b) Find the acceleration after 1 s
Differentiate the function and simplify the answer:
2.1 𝑓 (𝑥 ) =
–
2.2 ℎ (𝑥 ) =
Differentiate: 3.1 𝑦=𝑒 cos 4𝑡
3.2 𝑦 = tan(sin 𝑥)
–
3.3 𝑦 = 10
Find by implicit differentiation: 4.1 𝑥𝑒 = 𝑥 − 𝑦
4.2 4 cos 𝑥 sin 𝑦 = 1
5.1 Find the derivative of 𝑦 = tan √𝑥 in terms of x
5.2 Differentiate: a) ℎ(𝑥) = √𝑥
b) 𝑔(𝑥 ) = ln(sec 𝑥 + tan 𝑥)
, ANSWERS
1.1 𝑦 = 𝑥 + 2𝑥 − 𝑥 and the point (1; 2)
𝑦 = 4𝑥 + 4𝑥 − 1
𝑚 =7
Equation of tangent at (1; 2):
𝑦 − 2 = 7(𝑥 − 1)
𝑦 = 7𝑥 − 5
1.2
a) 𝑣 = 4𝑡 − 6𝑡 + 2𝑡 − 1
𝑎 = 12𝑡 − 12𝑡 + 2
b) 𝑎 = 2 𝑚. 𝑠
2.1 𝑓(𝑥) =
( ) ( )
𝑓 (𝑥) =
( )
=
( )
=
( )
=
2.1 ℎ(𝑥) =
( ) ( )
ℎ (𝑥) =
=
=
=
= cos 𝑥 + sin 𝑥
