MTH301 Assignment # 1 Solution Semester Fall 2012

Semester Fall 2012 Calculus II (MTH301) Assignment # 1

Q.1

Find the distance between the two points P(3,4,5) and (6,,7,8)

Solution:

Distance between two points P(3, 4 , 5) and (6, 7 ,8)

Distance formula

R^2 = ( x2-x1)^2+(y2-y1)^2+(z2-z1)^2

 R^2 = (6-3)^2+(7-4)^2+(8-5)^2

        = 3+3+3

        = 9           Ans...

Q.2

Find the cosines of the direction of angles of A=(-1,1,1) in

Solution:

Q.3

Convert the Cartesian coordinates (12, 5) in Polar Coordinates

Solution:

X=12
Y=5







Cartesian coordinate (12,5) is equal to Polar coordinate (13,22.6)

Q.4

Evaluate the limit  

Solution:

Along  x axis       y=0        

Along   y axis      x=0        

When    y=x

So limit not exist

Q.5

Evaluate the limit  

Solution:

Limit exist

Q.6

Find and  if     

With respect to     x

With respect to y