Calculus
Solve those problems with 12 h
Take-home Exam test
MA102
Dr. Ali Yousef
Instruction: Please solve the following problems showing the logical steps.
Each part worth 5 points.
Q1. a. Find the area of the region that lies inside π = 1 + πππ (π) and outside π = 2 β πππ (π).
b. Determine the arc-length of the function π = 1 + πππ (π) from 0 β€ π β€
π
3
.
c. Find the slope of the tangent line of the graph π = 1 + πππ (π) at π =
π
4
.
d. Find the equation of the tangent line of π = 1 + πππ (π) at π =
π
4
.
Q2. Consider the parametric equations given by:
C: π₯ = 3 β πππ 3(π‘) π¦ = 4 + π ππ(π‘) , π‘ β [0, π]
a. Eliminate the parameter π‘, and find a relation between π₯ πππ π¦.
b. Find the arc length of the parametric curve.
c. Determine the area under the curve given by the parametric equations.
Q3. Determine the surface area of the solid obtained by rotating the parametric curve about the π₯ β
ππ₯ππ . C: π₯ = πππ 3(π‘) π¦ = π ππ(π‘) , π‘ β [0,
π
2
].
Q4. Determine the equation of the tangent line to the parametric curve at the point (2, 0).
C: π₯ = π‘2 + 1 π¦ = π‘3 β π‘
Good Luck