Math Answers

.Find the length of the arc of the hyperbolic spiral rθ = a lying between r= a and r= 2a

If y= tan inverse x , obtain an equation showing the relationship between y n+2, y n+1 and yn

) An efficiency study of the workers at a factory shows that an average worker who comes to work at 8:00 am will have produced Q(t) = -t^3+9t^2+12t hours later. At what time during the morning is the worker performing most efficiently.

Sketch the graph of the function f defined by f(x) = x^4+ 8x^3 clearly giving all the properties used in it.

Obtain the largest possible domain and range of the function f, defined by f(x) = under root x+1 /x+2. Further, check whether or not lim x tends to a f(x) exists for x= 2, -1

Check the continuity of f(x)={x+1,xis smaller than 1
{ 0, 1greater than equal to x greater than equal to 2
{2-x , x greater than equal to 2
for all points in its domain.

Give an example each with justification, of a function defined on ]1, -1[which is
i) one-one but not onto.
ii) onto but not one-one.

Show that lim x tends to infinity=2/x-3=0

Find the volume and surface area of the solid formed by revolving a right-angled triangle about a side adjacent to the right angle. What is the solid so obtained

8. a) Define two partition P1 and P2 of ] [ such that 2, 5 P1 ⊂ P2 . Find the upper and lower
product sums with respect to f , defined by
⎩
⎨
⎧
− ≥
< = 1 x , x 4
x, x 4
f(x) 2 . Also verify the
relationship between these 4 sums. (4)
b) Derive a reduction formula for ∫( n x) dx, m∈N m l . Hence evaluate ∫( n x) dx 4 l . (4)
c) Find the approximate value of 5/3 ( upto 3 decimal places.