Assignment #  2

MTH301 (Spring 2011)

 Total marks: 10

Lecture # 9 to 15

Due date:  02/05/2011

DON’T MISS THESE Important instructions:

• Only Question # 1 is graded. Remaining questions are for your practice only therefore, you do not need to send the solution of non-graded questions.
• Upload assignments properly through LMS, (No Assignment will be accepted through email).
• All students are directed to use the font and style of text as is used in this document.
• This is an individual assignment, not group assignment, so keep in mind that you are supposed to submit your own, self made & different assignment even if you discuss the questions with your class fellows. All similar assignments (even with some meaningless modifications) will be awarded zero marks and no excuse will be accepted. This is your responsibility to keep your assignment safe from others.
• Above all instructions are for all assignments so may not be mentioned in future.
• Solve the assignment on MS word document and upload your word (.doc) files only.

Question 1:

Find a unit vector in the direction in which the function increases most rapidly at P(4,-3)

 Question 2:

 Find the equations of tangent plane and normal line to the surface z=e^3y sin3x  at the point.

 Question # 3

 Check whether the sphere x²+y²+z²= a²  and the cone z²= x²+y  are orthogonal or not.

 Question # 4:

 The length, width and height of a rectangular box are measured to be 3cm, 4cm and 5cm respectively, with a maximum error of 0.05cm in each measurement. Use differentials to approximate the maximum error in the calculated volume.

 Question # 5

 Given  f (x,y) = 3x²-6xy+3xy² Find local extrema and saddle points for the given function.