Scribd
Upload
117 views1 page

Assignment 2

The document is an assignment from the Department of Mathematics at Babu Banarasi Das National Institute of Technology & Management in Lucknow, India. It contains 12 problems related to differential calculus, functions, errors, maxima and minima. Students are asked to evaluate expressions, show relationships between variables, find errors in measurements, test functions for extrema, and minimize expressions under given constraints.

Uploaded by

harish nigam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
117 views1 page

Assignment 2

The document is an assignment from the Department of Mathematics at Babu Banarasi Das National Institute of Technology & Management in Lucknow, India. It contains 12 problems related to differential calculus, functions, errors, maxima and minima. Students are asked to evaluate expressions, show relationships between variables, find errors in measurements, test functions for extrema, and minimize expressions under given constraints.

Uploaded by

harish nigam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 1

Department of Mathematics

Babu Banarasi Das National Institute of Technology & Management, Lucknow

EAS 103 Engineering Mathematics I: B. Tech. (First Semester) – 2012-13

Assignment II (Differential Calculus - II)

( , )
1- If = , = then evaluate ( , )
.

∂ ( x, y, z )
2- If x = r sin θ cos ϕ , y = r sin θ sin ϕ , z = r cosθ , show that = r 2 sin θ .
∂(r , θ , ϕ )
x2 x3 xx xx ∂( y1 , y 2 , y 3 )
3- If y1 = , y 2 = 1 3 , y 3 = 1 2 , then show that = 4.
x1 x2 x3 ∂(x1 , x 2 , x3 )
4- If = , = + + , = + + ( , , ).
5- If u , v , w are the roots of the cubic (λ − x )3 + (λ − y )3 + (λ − z )3 = 0 in λ , find
J(u,v,w).

6- If u = sin −1 x + sin −1 y , v = x 1 − y 2 + y 1 − x 2 , Is u and v functionally related?


If so, find the relationship.
l
7- The period of a simple pendulum is T = 2π . Find the maximum error in T
g
due to the possible errors upto 1% in l and 2.5% in g.
8- A balloon is in the form of right circular cylinder of radius 1.5 meter and length
4m and is surmounted by hemispherical ends. If the radius is increased by 0.01m
and the length by 0.05m, find the percentage change in the volume of the balloon
9- If Δ be the area of a triangle , prove that the error in Δ resulting from a error in c
∆ 1 1 1 1 
is given by δ∆ =  + + − δc.
4  s s − a s − b s − c 
10- In estimating the number of bricks in pile which is measured to be 5m×10m×5m
the count of bricks is taken as 100 bricks per m 3 . Find the error in the cost when
the tape is stretched 2% beyond its standard length .The cost of bricks is Rs 2000
per thousand bricks.
11- Test the function f ( x, y ) = x 3 y 2 (6 − x − y ) for maxima and minima for point not
at the origin.
12- Find the minimum value of + + , given that + + =

You might also like