Math 105, Midterm exam (2)
Almajma’ah University
Math 105
Engineering College
5/2/1431
Name:
Level 2:
Academic Number:
Time allowed: 90 min.
Midterm Exam (2)
Question 1:
Find:
a.
𝑙𝑖𝑚
𝑥 2 +𝑥+7
𝑥→∞ 2𝑥 2 +3𝑥+4
3𝑥+𝑠𝑖𝑛3𝑥
b. 𝑙𝑖𝑚
𝑥→0 𝑠𝑖𝑛 𝑥+𝑡𝑎𝑛 4𝑥
Question 2:
Find a and b so that the following function will be defined at all points
𝑥+1
𝑓𝑜𝑟 𝑥 < 1
𝑓𝑜𝑟 1 ≤ 𝑥 < 2
c. 𝑓(𝑥) = {𝑎𝑥 + 𝑏
3𝑥
𝑓𝑜𝑟 𝑥 ≥ 2
Question 3:
See if the following function is continuous or not, if not mention the type
of discontinuity.
1 ;

f ( x)   1 ;
c ;

x 2
x2
x2
Question 4:
Find the instant rate of change for the area of a circle with respect to its
radius. Then find this rate when the radius equal to 3
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Math 105, Midterm exam (2)
Question 5:
Find
𝒅𝒚
𝒅𝒙
d.
𝑥 3 − 2𝑥𝑦 + 𝑦 2 = 6𝑦
e. 𝑦 = 𝑥 3 √𝑥 2 + 𝑥 + 1
f.
𝑦 = (𝑥 3 + 𝑡𝑎𝑛 𝑥)6
Question 6:
a) If 𝑓(𝑥) = 𝑥 2 − 4𝑥 + 1 Find all the real number c that satisfy “Rolle’s
Theorem” in the interval [0,4].
b) Use the definition of the first derivatives to find the first derivative of:
f(x) = x2 + 2
Best Wishes
Dr. SaMeH
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