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

(a)

0.2%

(b)

0.4%

(c)

0.04%

(d)

0.08%

The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

(a)

\(\frac{1}{31}\)

(b)

\(\frac15\)

(c)

5

(d)

31

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

(a)

0.4 cu.cm

(b)

0.45 cu.cm

(c)

2 cu.cm

(d)

4.8 cu.cm

The change in the surface area S = 6x² of a cube when the edge length varies from x_o to x_o+ dx is

(a)

12 x_o+dx

(b)

12x_o dx

(c)

6x_o dx

(d)

6x_o+ dx

If \(g(x, y)=3 x^{2}-5 y+2 y^{2}, x(t)=e^{t}\) and y(t) = cos t, then \(\frac{dg}{dt}\) is equal to

(a)

6e^2t + 5 sin t - 4 cos t sin t

(b)

6e^2t- 5 sin t + 4 cos t sin t

(c)

3e^2t+ 5 sin t + 4 cos t sin t

(d)

3e^2t - 5 sin t + 4 cos t sin t