MTH301 Quiz 2 by Attiq Kundi

MTH-301 Quiz File 2 · By KNOWLEDGE FOR US · Attiq Kundi

1. The rose curve has 2n-equally spaced petals of loops if n it’s____

Answer: Even.

2. In 3-space, r(t)I + y(t)j + z(t)k, is smooth function of t if x’(t), y’(t), z’(t) are____and there is no value of t at which all three derivatives are zero.

Answer: Continuous.

3. The position of the limacon relative to the polar axis depends on whether____appears in the equation and whether + or – occurs.

Answer: (d) Both (a) or (b).

4. Equation of the tangent line of vector valued function r(t) at r(t0) is

Answer: r=r (t0) + tr’ (t0)

5. The point (3, 1890) and the point___are the same in polar system.

Answer: (-3,1890)

6. The graph of r=(1+t)i + (-3t)j +(2+4t)k is the

Answer: line parallel to the vector i - 3j + 4k.

7. For a vector function r(t) = √2𝑡 i + (t+1) j-k then length of r(t).

Answer: ||r (t) ||√𝟐𝒕2

8. The Lemniscate are centered at the origin, but position relative to the polar axis depends on the sign preceding the a2 and whether___appears in the equation.

Answer: (d) Both (a) or (b).

9. In polar coordinate system, x axis is also called

Answer: Polar axis

10. In polar coordinates, R

Answer: G f

Answer: Polar angle of p.

12. The orientation of the rose relative to the polar axis depends on the sign of the constant a and whether___appears in the equation.

Answer: (d) Both (a) or (b).

Answer: spiral with a=1

14. In the integration of polar coordinates dxdy is replaced by ___.

15. 0 0 0 x y z dx dy dz 

Answer: 1

16. The equation of the form:

Represent flower – shaped curves called_____.

Answer: roses.

17. The equation, 4cos2 , r represent a____.

Answer: Lemniscate

18. In polar coordinate system, the equation 𝑟= 𝑎 represents a circle with center at____.

19. R Can be expressed in polar coordinates as____.