WorksheetsTLA 5.1 Calculus
Total questions: 15
Worksheet time: 45mins
Differentiate y = sec (x^2 + 2).
2x cos (x^2 + 2)
–cos (x^2 + 2) cot (x^2 + 2)
2x sec (x^2 + 2) tan (x^2 + 2)
cos (x^2 +2)
What is the derivative with respect to x of (x + 1)^3 – x^3?
3x + 6
3x – 3
6x – 3
6x + 3
If y = (t2 + 2)^2 and t = x^(1/2), determine dy/dx.
3/2
(2x^2 + 2x) / 3
2(x + 2)
x^(5/2) + x^(1/2)
Differentiate the equation y = x^2 / (x + 1)
(x^2 + 2x) / (x + 1)^2
x / (x + 1)
2x
(2x^2) / (x + 1)
Find the slope of the line tangent to the curve y = x^3 – 2x + 1 at x = 1.
1
1/2
1/3
1/4
Find the minimum distance from the point (4, 2) to the parabola y^2 = 8x.
4√3
2√2
√3
2√3
A farmer has enough money to build only 100 meters of fence. What are the dimensions of the field he can enclose the maximum area?
25 m x 25 m
15 m x 35 m
20 m x 30 m
22.5 m x 27.5 m
Determine the diameter of a closed cylindrical tank having a volume of 11.3 cu m. to obtain minimum surface area.
1.22
1.64
2.44
2.68
A fencing is limited to 20 ft. length. What is the maximum rectangular area that can be fenced in using two perpendicular corner sides of an existing wall?
120 ft^2
100 ft^2
140 ft^2
190 ft^2
A function is given below, what x value maximizes y?
y^2 + y + x^2 – 2x = 5
2.23
-1
5
1
What is the integral of (3t – 1)^3 dt?
(1/12)(3t – 1)^4 + C
(1/12)(3t – 4)^4 + C
(1/4)(3t – 1)^4 + C
(1/4)(3t – 1)^3 + C
Integrate: (7x^3 + 4x^2) dx
(7x^3/3) + (4x^2/2) + C
(7x^4/4) + (4x^2/5) + C
(7x^4/4) + (4x^3/3) + C
7x^4 + (4x^2/2) + C
Find the area bounded by the curve y = x^2 + 2 and the lines x = 0 and y = 0 and x = 4.
88/3 sq. units
64/3 sq. units
54/3 sq. units
64/5 sq. units
What is the area (in square units) bounded by the curve y^2 = 4x and x^2 = 4y?
5.33 sq. units
6.67 sq. units
7.33 sq. units
8.67 sq. units
Find the centroid of the area in first quadrant bounded by the curve y^2 = 4ax and the latus rectum.
(0.6a, 0.75a)
(1.23a, 0.95a)
(0.94a, 2.97a)
(1.16a, 0.53a)
