MTH301 Quiz by Knowledge for Us

MTH-301 Quiz File · By Knowledge for us · Attiq Kundi

Q1. Which integral gives the arc length of the curve?

r t t i tj t k

Answer: (1 t dt

2. A single curve can be represented by:

Answer: Only two vector-valued function

3. The differential equation, (2 3) (6 1) dz x xy dx y x dy is an exact

differential equation.

Answer: False

4. If r is a vector-valued function in 2-space or 3-space, then

d

r t dt

dt

Answer: ( ) r t

5. If ( ) r t d

t i t j then r t

dt

Answer: i j

6. The arc length of the potation of the circular helix where ( / dt) dx sin ,(dy/ dt) cos t t

and ( dz dt  and 0

t  π, then the arc length is

Answer: L dy

7. For a vector valued function ( ) r t t 1) i t j then length of ( ) r t

Answer: 1) r t t t

8. For a vector valued function ( ) r t t 1) i t j then length of ( ) r t

Answer: 1) r t t t

9. Let r t t i t ,j then (1) 9 . r i j

Answer: True

10. Natural domain of a vector valued function is_____.

Answer: intersection of the natural domains of its components.

11. If x t y t and z t are continuous for a t b then the arc length for the given

parametric equations ( ),y y(t),z z(t);(a t b)is x x t

Answer: (dy/ dt) b

a L dx dt dx dt dt

12. The differential dz of the function z x y is:

Answer: dz xdx ydy

13. A vector-valued function is continuous at some point 10 if:

Answer: each of its components is continuous at that point.

14. If r t t i t j t k then d

r t

dt

Answer: t i j k

15. If

r t t i t j then r t dt 

Answer: t i t j C j

16. The differential equation, (2 dz xydx x y dy is an exact differential equation.

Answer: False

17. If '( ) x t and y'(t) are continuous for a t b, then the given parametric equation are:

Answer: ( );(a t b) x x t y y t

18. Equation of the tangent line of vector valued function r( )t at r( ) t is:

Answer: r r( ) t t

19. The differential equation dz ydx xdy is an exact differential equation.

Answer: True.