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## #1 2019-12-29 07:22:54

Zeeshan 01
Member
Registered: 2016-07-22
Posts: 746

### Calculus MCQS IMPORTANT

Question1 : if the function fxx(x0,y0)>0 then f has a ------ at (x0,y0)

a) Relative minima     b) relative maxima  c) saddle point    d) none

Question2 : if phi=2xz^4-  (x^2y) , the |delta phi | at point (2,2,-1) is

a) 2sqrt93     b) sqrt 372  c) 2sqrt91    d) both a and b

Question 3 : if y=f(x) has continuous derivatives on [a,b] and s denotes the length of arc between the lines x a and x  b then

Question 4 :  arc length s=integral a to b   sqrt(r^2+(dr/d thetha)^2 ) d thetha is called

a) Rectangular Coordinates   b)  polar coordinates   c ) spherical coordinates   d) none

Question 5 : if the two vectors are A=3i+4j+k   and B=i-j+k then

a)They are orthogonal   b) orthonormal   c) antiparallel   d) none

Malik

Offline

## #2 2019-12-29 22:34:46

Bob Registered: 2010-06-20
Posts: 9,271

### Re: Calculus MCQS IMPORTANT

hi Zeeshan 01

Haven't heard from you for a while.  You seem to have made good progress if you are on to topics like these.  Well done!

There's no need to put the word IMPORTANT into your titles.  I treat all requests for help as equally important and try to help if I can.

Question 5 : if the two vectors are A=3i+4j+k   and B=i-j+k then

a)They are orthogonal   b) orthonormal   c) antiparallel   d) none

Question 9 :   The angle between Vectors   -2i+3j+k  and i+2j-4k is
a) 0 degree           b)  90 degree    c) 180 degree

Two vectors, A and B are parallel if there is a constant, k,  such that A = kB.  If k is positive then the vectors go in the same direction so the angle between them is 0.  If k is negative then they go in opposite directions, so I suppose you could say the angle between them is 180, although I've never met this in a question before.

If the dot (or scalar) product is 0, then they are at right angles, so the angle between them is 90.  Orthogonal is just another way to say this.  If the vectors are orthogonal and unit vectors then they are orthonormal.  Use Pythagoras to determine whether they are unit vectors.

Question1 : if the function fxx(x0,y0)>0 then f has a ------ at (x0,y0)
a) Relative minima     b) relative maxima  c) saddle point    d) none

I don't understand the notation here 'fxx'.  Did you mean f(x,y) ?  If so then none of the answers can be chosen since any could be true.  If 'fxx' means the double differentiated functions then, as with the 2D case, this would be a local minimum.

Question 8 :    If function fxx(x0,y0)=0 then f has a -----  at (X0,y0)
a) relative minima        b ) relative maxima   c) saddle point

This seems to be the same question again.

Question2 : if phi=2xz^4-  (x^2y) , the |delta phi | at point (2,2,-1) is
a) 2sqrt93     b) sqrt 372  c) 2sqrt91    d) both a and b

Sorry, what does ' the |delta phi | ' mean?

Question 3 : if y=f(x) has continuous derivatives on [a,b] and s denotes the length of arc between the lines x a and x  b then

Question incomplete.

Question 4 :  arc length s=integral a to b   sqrt(r^2+(dr/d thetha)^2 ) d thetha is called

a) Rectangular Coordinates   b)  polar coordinates   c ) spherical coordinates   d) none

Is thetha meant to be θ ?  That looks like polar coordinates r and θ to me.  I don't think spherical as another angle would be required.

Question 6:  If phi =1/(r^2)   then (delta)^2  phi is

What does '(delta)^2 ' mean?
a) 1                         b) -1                c) 0          d)1/(r^2)

Question 7:   If f(x,y)=1 throughout the region D then I=integral integral dx dy represents

a) Volume   b) Arc        C)  bounded below          d) bounded above

Imagine a 3D graph with x,y in the horizontal plane and z values above.  If f is constant then the graph of f is a plane parallel to the x,y plane, one unit higher in the xz direction.  If you integrated in 2 directions you would get the volume below the graph.

Please post back clarifying questions 2,3 and 6.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob Offline