MCQs

Let f (x) = $\sqrt[3]{x}$ . Find the linear approximation at x = 27 . Use the linear approximation to approximate $\sqrt[3]{27.2}$
1. 3.0074
2. 3.74
3. 3.074
4. 5.004
The radius of a circular plate is measured as 12 65. cm instead of the actual length 12 5. cm.
find the Absolute error in calculating the area of the circular plate.
1. 0.0225
2. 0.25
3. 0.022
4. 0.225
The radius of a circular plate is measured as 12 65. cm instead of the actual length 12 5. cm.
find the Relative error in calculating the area of the circular plate.
1. 0.06
2. 0.07
3. 0.0006
4. 0.006
The radius of a circular plate is measured as 12 65. cm instead of the actual length 12 5. cm.
find the Percentage error in calculating the area of the circular plate.
1. 0.6
2. 0.06
3. 0.0006
4. 0.1
A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to
9 8. cm. Find approximations for the change in the volume.
1. volume increases by 80 pie
2. volume increases by 50 pie
3. volume increases by 20 pie
4. volume increases by 120 pie
A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to
9 8. cm. Find approximations for the change in the surface area.
1. surface decreases by 20 pie
2. surface decreases by 25 pie
3. surface decreases by 16 pie
4. surface decreases by 15 pie
The trunk of a tree has diameter 30 cm. During the following year, the circumference grew
6 cm. Approximately, how much did the tree’s diameter grow?
1. 6
2. 6/pie
3. 6/7
4. 5/pie
The trunk of a tree has diameter 30 cm. During the following year, the circumference grew
6 cm.What is the percentage increase in area of the tree’s cross-section?
1. 40/pie
2. 20/pie
3. 10/pie
4. 5/pie
An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is 5mm and radius to the outside ofthe shell is 5.3 mm, find the volume of the shell approximately.
1. 5pie
2. 10pie
3. 15pie
4. 30pie
A circular plate expands uniformly under the influence of heat. If it’s radius increases from 10.5 cm to 10.75 cm, then find an approximate change in the area and the approximate percentage change in the area.
1. 5.25pie, 4.76 percentage
2. 5.25pie, 4.7 percentage
3. 5.2pie, 4.76 percentage
4. 5.25pie, 4.6 percentage
A coat of paint of thickness 0 2. cm is applied to the faces of a cube whose edge is 10 cm.
Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube.
1. 60,61.2
2. 50,61.2
3. 60,71.2
4. 40,6.2
Find the partial derivatives of the functions at the indicated points.
f (x, y) = $3 x^{2} - 2 x y + y^{2} + 5 x + 2$ ( 2, -5)
1. 27,14
2. 27,-14
3. 23,14
4. 23,-14
A circular template has a radius of 10 cm. The measurement of radius has an approximate
error of 0.02 cm. Then the percentage error in calculating area of this template is
1. 0.2%
2. 0.4%
3. 0.04%
4. 0.08%
If f (x , y, z ) = xy+ yz + zx , then $f_{x} - f_{z}$ is equal to
1. z -x
2. y -z
3. x- z
4. y- x
The approximate change in the volume V of a cube of side x metres caused by increasing
the side by 1% is
1. 0 .3 xdx $m^{3}$
2. 0 .03 x $m^{3}$
3. 0.03 $x^{2} m^{3}$
4. 0.03 $x^{3} m^{3}$
If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our
calculation of the volume is
1. 0.4 cu.cm
2. 0.45 cu.cm
3. 2 cu.cm
4. 4.8 cu.cm
The percentage error of fifth root of 31 is approximately how many times the percentage
error in 31?
1. 1/31
2. 1/5
3. 5
4. 31

MCQs

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