Ques1) Let g(x) = {log(1+x)} -1 - x-1 , where x>0, then
(a) 1<g(X)<2 (b) -1<g(x) <0 (c) 0<g(X)<1 (d) none of these
Ques2) Show that the interval in which x3 increses more rapidly than 6x2+15x+5 is (5,infinity).
Ques3) If f(x)=x/sinx and g(x) = x/tanx where 0<x≤1 ,then show that f(x) is inc whereas g(x) is dec.
Ques4) If tan(pie cos @) = cot (pie sin@) where 0 <@<pie/2 and f(x) = (cos@ + sin@)x , then find the interval in which f(X) is inc and dec.
Ques5) Using L.MV.T theorm, prove that
x - (x3/6) , sinx , x where 0 < x ≤ pie/2
11Ques 1
ans is C
Use log(1+x)/x=1 when x->0
Ques 2
3x2-12x-15>0
(x-5)(x+1)
So whats the problem here?
Ques 3
straight forward :|
take derivative
Ques 4
tan(∩cos@)tan(∩sin@)=1
hint here is sin@=cos(∩/2-@)
use it above and solve
tahe deivative of f(x) = (cos@ + sin@)x and check for increasing and decreasing
Ques 5
NOT CLEAR :|
