Fileclaine20jasmin20nacisdocumentsellaineie19820

[26/05/2020 12:16:32 AM]
d. Perpendicular
91. Find the slope of the line defined by c. 1
Basic Engineering Correlation (Calculus Reviewer)
1. The depth of water in cylindrical tank 4 m in diameter is increasing at the rate of 0.7 m/min. Find the rate at which the
water flows into the tank.
d. 8.8
2. The volume of the sphere is increasing at the rate of 6 cm3 / hr. At what is its surface area increasing (in cn2/hr) when
the radius is 50cm?
b. 0.24
3. Find the height of aright circular cylinder of maximum volume, which can be inscribed in a sphere of radius 10 cm.
b. 11.55 cm.
4. find the area in the first quadrant bounded by the parabola y2 = 4x, x = 1 and x = 3
c. 5.595
5. Find the maximum point of y = x + 1/x
c. (-1, -2)
6. ___________ is the concept of finding the derivative of composite functions.
d. Chain Rule
7. Find the area bounded by the curve defined by the equation x2 = 8y and its latus rectum.
b. 32/3
8. If y = x lnx. Find
b. 1/x
9. Car A moves due east at 30 kph, at the same instant car B is moving S 30o E with the speed 60 kph. The distance
from A to B is 30 km. Find how fast is the distance between them separating after 1 hour
c. 45 kph
10. A box is to be constructed from a piece of zinc 20 sq. in. by cutting equal squarea from each corner and turning up
the zinc to form the side. What is the volume of the largest box that can be so constructed?
a. 592.59 cu. in.
11. Find the coordinates of the vertex of the parabola y = x2 - 4x + 1 by making use of the fact that at the vertex, the
slope of the tangent is zero.
d. (2, -3)
12. Given the function f(x) = x3 - 6x +2. Fnd the first derivative at x = 2
c. 6
13. If the first derivative of the function is constant, then the function is__________.
b. Logarithmic
14. Using the two existing corner sides of an existing wall, what is the maximum rectangular area that can be fenced by
a fencing material 30 ft. long?

[26/05/2020 12:16:32 AM]
b. 225 sq.ft.
15. The velocity of a body is given by v(t) = sin(xt), where the velocity is given in meters per second and " t " is given in
seconds. The distance covered in meters between t =1/4 and 1/2 second is close to
d. 0.2551 m
16. Differentiate y = ex cos x2
a. ex(cosx2 - 2x sinx2)
17. Three sides of a trapezoid are each 8 cm. long. How long is the fourth side when the area of the trapezoid has the
greatest value?
c. 16
18. Differentiate y = sec(x2 + 2)
d. 2xsec(x2 + 2)tan(x2 + 2)
19. A statue 3 m high is standing on a base of 4 m high. If an observer's eye is 1.5 m above the ground, how far should
he stand from the base in order that the angle subtended by the statue is a maximum.
d. 3.71 m
20. What is the area of the largest rectangle that can be inscribed in a semi-circle of radius 10?
b. 100
21. Find the partial derivative with recpect to x of the funcyion xy2 - 5y + 6
d. y2
22. In the curve 2 + 12x - x3, find the critical points.