19yes, the book also says (b) is the answer ! great work ! hurrah ![1]
if the function 0∫x f(t) dt->5 as |x|->1,then the value of (a) so that the equation 2x + 0∫x f(t) dt =a has atleast 2 roots of opposite sign in (-1,1) is
(a) a ε (0,1) (b) a ε (0,3) (c) a ε (-1,∞) (d) a ε (3,∞)
.....may be i am missing something vital ,here ![2]
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2 Answers
62at x=-1, the function 2x+0∫x f(t) dt tends to 3
while at x=1, the function 0∫x f(t) dt tends to 7
at x=0, the function is zero..
so for a root, one -ve and one +ve a should lie between 0 and 3
think in terms of the graph.
I am assuming that the function is continuous which is somehow not given here!
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