Sir Syed CASE Institute of Technology, Islamabad
Assignment#1
SC1001 Calculus & Analytical Geometry
BSCS, BSSE
Total Marks 100
Instructor: Dr Iqra Shahzadi
Due Date: 2-11-2021 (12 AM)
Q#1
Sketch the graph of piece-wise function defined by
0
𝑓(𝑥) = {√4 − 𝑥 2
𝑥
𝑥 ≤ −2
−2<𝑥 <2
𝑥≥2
Q#2
Find the natural domain of
i)
ii)
iii)
iv)
v)
Q#3
𝑓(𝑥) = √𝑥 2 − 5𝑥 + 6
𝑓(𝑥) = tan 𝑥
𝑥
𝑓(𝑥) = |𝑥|
𝑓(𝑥) = (sin √𝑥)−2
1
𝑓(𝑥) =
1−sin 𝑥
Use the equation 𝑦 = 1 + √𝑥 to answer the following questions.
i)
ii)
iii)
For what value of 𝑥 is 𝑦 = 4?
For what value of 𝑥 is 𝑦 = 0?
For what value of 𝑥 is 𝑦 = 6?
Q#4
A construction company has adjoined a 1000𝑓𝑡 2 Rectangular
enclosure to its office building. Three sides of the enclosure are faced
in. The side of the building adjacent to the enclosure is 100ft long
and portion of this side is used as the fourth side of the enclosure.
Let 𝑥 and 𝑦 be the dimensions of the endosure, where 𝑥 is measured
parallel to the building and let L be the length of fencing required for
those dimensions.
i)
ii)
iii)
Q#5
Find the formula for L interns of 𝑥 and 𝑦.
Find the formula that expresses L as a function of 𝑥 above.
What is the domain of function in part ii.
Express f as a composition of two functions, that is find 𝑔 and ℎ such
that
𝑓 = 𝑔𝑜ℎ
i)
ii)
Q#6
𝑓(𝑥) = 3 sin 𝑥
3
𝑓(𝑥) =
5+cos 𝑥
Sketch the graph of
i)
ii)
Q#7
𝑓(𝑥) = 𝑥 2
𝑓(𝑥) = sin 𝑥
Sketch the graph by translating and reflection.
i)
ii)
iii)
iv)
𝑦 = 3 − √𝑥 + 1
1
𝑦=
𝑥−3
𝑦 = 𝑥 2 + 6𝑥
3
𝑦 = 2 + √𝑥 + 1
Q#8
According to the coulomb’s law the force F of attraction between
positive and negative charge in inversely proportional to the square
of distance 𝑥 between them.
i)
ii)
iii)
Assuming that the force of attraction between two point
charges is 0.0005 newton when the distance between them
is 0.3 meter, find the constant of proportionality.
Find the force of attraction between the point charges when
they are 3 meters apart.
Make the graph of force versus distance for the two charges.
(THE END)