MTH301 Quiz 2 Updated 2021

MTH301 Quiz 2 2021

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1. For a function r(t) = x(t)I + y(t)j in 2-space we define limt- >ar(t)=_______.

(limt->a x(t))i + (limt->y(t))j….confirm from handouts

2. For a function r(t) = x(t)I + y(t)j+z(t)k in 3-space we define limt- >ar(t)=_______.

(limt->ax(t))i+(limt→αy(t))j+(limt→αz(t))k….confirm from handouts

3. In 2D-space the parametric equation x= x(t), y=y(t) can be expressed in single vector equation

r(t)= x (t)i + y (t) j………confirm from handouts

4. If a point p(r, θ) in polar coordinate system, then r is the distance of p from the

None of these……confirm from handouts · 5. Graph of c = x0i+y0j+z0k · Is the curve passing through the point (x0,y0,z0)

6. The vector r is continuous at t0 if _________.

 r (t0) is defined

 r(t) exists

 limt→t0ts; r(t) = r (limt→t00). …….. All options ….confirm handouts

7. The relation between the polar coordinates (r, θ) and the rectangular coordinates (x,y) is given by __________.

x = r cos θ, y = r sin θ……...confirm from handouts

8. Graph of a vector-valued function can fail to have a tangent vector at a point because

does not exist or because the derivative is zero at the point………both options………confirm from handouts

9. The equations of the form · r= asin nθ · r=acos nθ

represent flower – shaped curves called _______.

Roses…..confirm from handouts

10. The roses curve has 2n-equally spaced petals of loop if n is ____.

Even…..confirm from handouts · 11. r(t) = x(t)i + y(t)j · is a vector valued function…..confirm from handouts · 12. Vector valued function has

domain consists of real numbers and the range consists of vectors……confirm from handouts

13. Real valued function has

Domain and range are sets of real number…..confirm from handouts

14. If p(r, θ) is a point in polar coordinate system, then θ is called

polar angle of P

15. The arc length of the portation of the circular helix where (dx/dt) = -sint, (dy/dt) = cost and (dz/dt)=1 0 < t < pi, then the arc length is

L = ∫(under root(2)dt)…..confirm form handouts

16. If r(t) = t2i + tj + 3tk, then d/dt(r(t)=________.

2ti + j + 3k……confirm · 17. The equation r= a(1 + cos θ) respresents _______ · Cardioid……..confim from handouts

18. A parametric curve in 2-space or 3-space is called _____ if it is the graph of some smooth vector-valued function.

Smooth…..confirm from handouts · 19. The point p(r, θ) in polar coordinate system lies on · Polar axis….confirm from handouts

20. The point (3, 1890) and the point ___________ are the same in polar system.

(-3, 90)

21. Give the integral ∫∫ f(x,y) dxdy, can be expressed in polar coordinates as _________ where a< θ < b and c < r < d

b d a c f r drd

22. IF r(t) = x(t)i + y(t)j +z(t)k is a vector – valued function in 3-space, and if x(t), y(t) and z(t) are differentiable, then d/dt [r(t)] = _________.