MTH301 Quiz 2 Set 2

Q1. Evaluation of \int\limits_0^1 {\int\limits_0^2 {{x^2}ydxdy} } is ___________.

1. 4/3
2. 1/3
3. 2/3
4. 8/3

Correct answer: 4/3

Q2. What does the order of integration refer to in double integrals?

1. The type of region being integrated.
2. The sequence in which variables are integrated.
3. The size of the region of integration.
4. The number of iterations required.

Correct answer: The sequence in which variables are integrated.

Q3. \eqalign{ & {\text{Let f be a function of two variables at a critical point}} (0,2), {f_{xx}}(0,2) = - 2, {f_{yy}}(0,2) = - 1 {\text{and}} {f_{xy}}(0,2) = 0 {\text{ }} \cr & {\text{so}} D = {f_{xx}}(0,2){f_{yy}}(0,2) - {f^2}_{xy}(0,2) = 2 \cr}

1. {{then}} {{f has a relative maximum at}} (0,2).
2. {{then no conclusion can be drawn}}{{.}}
3. {{then f has a saddle}} {{point at}} (0,2).
4. {{then f has a relative minimum at}} (0,2).

Correct answer: {{then}} {{f has a relative maximum at}} (0,2).

Q4. The volume of parallelepiped with dimensions x, y, z and height h is V=xyh

1. True
2. False

Correct answer: False

Q5. Which of the following equations represents a sphere in three-dimensional space?

1. {x^2} + {y^2} + {z^2} = {r^2}
2. {x^2} - {y^2} + z = {r^2}
3. {x^2} - {y^2} = {r^2}
4. {x^2} + {y^2} - 4y - {z^2} = {r}

Correct answer: {x^2} + {y^2} + {z^2} = {r^2}

Q6. What is the condition of the extreme value theorem?

1. A function must be continuous and differential
2. A function must be continuous on a closed interval
3. A function must be differentiable
4. No conditions are necessary

Correct answer: A function must be continuous on a closed interval

Q7. If the function f is continuous on the closed interval [a, b], then f has an absolute

maximum value and an

absolute minimum value on [a, b]

A. Rolle's Theorem B. Mean Value Theorem

C. Extreme Valued Theorem

D. Squeeze Theorem

Q8. Evaluation of \int\limits_0^1 {\int\limits_0^1 {dydx} } is ________.

1. 4
2. 2
3. 1
4. 0

Correct answer: 1