IIT JAM Follow
February 8, 2022 12:36 am 30 pts
The value of lim x-0 x 5 Let P(x)=| -1 for all xe R. 1. (a.) does not exist. Then which of the following statement(s) is(are) TRUE? (b.) is infinite. (Cc.) exists and equals 1. (a.) The equation P(x) =0 has exactly one (d.) exists and equals 0. solution in R Let f be a bounded function on R and (b.) P(x) is strictly increasing for all re R 2 ae R. For 8>0, let oa,8) = sup|s(x)-f (a). xela -8,a +8]. (c.) The equation P(x) =0 has exactly two Then solution R (a.) o(a,8,) S o(a, 82) if 8, s ô (d.) P(x) is strictly decreasing for all re R (6.) limg-0+ @(a, 8) =0 for all ae R. 6. The function f:R>R is given by (C.) lim0- o(a,8) need not exist. Sx)=e +l-1| Which of the following is true about the function f? (d.) lim 0- o(a.8) =0 if and only if f is (a.) It is not differentiable exactly at three continuous at a. points of R. Let f be a continuously differentiable that 3. (b.) It is not differentiable at x=0. function on R suppose L= lim (f x)+ f a)) exists. If 0
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