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Is the curve r = 2 sin 3theta symmetric about the
line theta = π/2 ? Justify your answer.
Find the volume of the solid of revolution
obtained by revolving the area under the
3 curve y = 2 + x^3
between x = 0 and x = 2
about the x-axis. Draw a rough sketch.
Find the length of the curve given by x = t^3,
y = 2t^2 in 0<= t/<=1. What is the slope of the
curve at t = 1/2 ?
Every continuous function is also
differentiable. True or False
Find the domain of the function
f(x) = √{(4-x^2)/ [x]+ 2}
Where [x] is greatest integer function
Find the area of a loop of the curve
r = a sin 3theta
trace the area between the curv'es r: = 2 and
r = 2 sin 3theta and thm find this area.
Check whether the function f, defined by
f(x) = cos x - cos 3x, is periodic or not.
Find the area of the loop of the curve,
x (x^2+ y^2) = a (x^2- y^2).
Trace the curve :
y^2(x+1) = x^2 (3-x),
Clearly stating all the properties used for
tracing it.
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