Suppose `p(x) = a_0 + a_1x + a_2x^2 +…+ a_nx^n`. If `|p(x)| le |e^(x-1) - 1| le 1` then prove |a1 + 2a2 +...... + n an| ≤ 1.

1/(x+2)le0

(x+1)/3le(2x-1)/4,x in R

If 0 le x le 1, then the minimum value of (x^(2) +x+1) is-

If (1+x-2x^2)^6=1+a_1x+a_2x^2+……+a_(12)x^12 then

If the function f(x) ={x+1 if x le 1 , 2x+1 if 1 lt x le 2 and g(x) = {x^2 if -1 le x le 2 , x+2 if 2 le x le 3 then the number of roots of the equation f(g(x))=2

If |a_1sinx+a_2sin2x++a_nsinn x|lt=|sinx| for x in R , then prove that |a_1+2a_2+3a_3+n a_n|lt=1

If (1+x+x^2)^n=a_0+a_1x+a_2x^2+.......+a_(2n)x^(2n) , then prove that a_0+a_2+a_4+....+a_(2n)=1/2(3^n+1) .

Let P(x)=a_0+a_1x^2+a_2x^4++a_n x^(2n) be a polynomial in a real variable x with 0 < a_0 < a_1 < a_2 <......< a_n . The function P(x) has a. neither a maximum nor a minimum b. only one maximum c. only one minimum d. only one maximum and only one minimum e. none of these

Solve (x)/(x+2) le (1)/(|x|)

Let f(x)=a_0+a_1x+a_2x^2+.....+a_nx^n+ ....and f(x)/(1-x)=b_0+b_1x+b_2x^2+.....+b_nx^n+ ...., then