Using L’Hospital’s rule find the limit of the following function
My Self Assessment
a) −1
The number of solutions of the equation xesinxcosx = 0 in the interval (0, π/2)
f (x) = x3/2 (3x – 10), x ≥ 0 then f (x) is increasing in
Consider the polynomial f (x) = 1 + 2x + 3x2 + 4x3. Let s be the sum of all distinct real roots of f (x) and let t = |s|. The real number s lies in the interval
a)
b)
c)
d)
If F (x) =
where = and and given that F (5) = 5 then F (10) is equal to
a) 5
b) 10
c) 0
d) 15
If f (x) = cos [π2] x + cos [-π2] x where [x] stands of the greatest integer function then
a) f = −1
c) f (−π) = 0
d) f = 1
Let f (x + y) = f (x) f (y) for all x, y. Suppose that f (5) = 2 and (0) = 3. Find f (5).
a) 1
b) 2
c) 3
d) 6
Let a + b + c = 0, then the quadratic equation has
a) at least one root in (0, 1)
b) one root in (2, 3) and the other in
c) imaginary roots
d) none of these
If f (x) =
a) f (x) is a strictly increasing function
b) f (x) has a local maxima
c) f (x) is a strictly decreasing function
d) f (x) is bounded
Suppose p(x) = If prove that
Determine whether the following statements are true or false. Statement 1 Statement 2 f (x) is continuous in [0, 2]
a) True, True
b) True, False
c) False True
d) False, False
In (- 4, 4) the function has
a) No extrema
b) One extrema
c) Two extremas
d) None of the above
The length of longest interval in which the function is increasing is
has
