Find the minimum value of `|x|+|x+1/2|+|x-3|+|x-5/2|dot`

Let f(x)=2cos e c2x+secx+cos e cxdot Then find the minimum value of f(x)forx in (0,pi/2)dot

Find the minimum value of 2^("sin" x) + 2^("cos" x)

Find the largest natural number a for which the maximum value of f(x)=a-1+2x-x^2 is smaller than the minimum value of g(x)=x^2-2a x+10-2adot

Find the minimum value of (x_1-x_2)^2+((x_1^2)/20-sqrt((17-x_2)(x_2-13)))^2 where x_1 in R^+,x_2 in (13,17) .

Solve |2x-3|+|x-1|=|x-2|dot

Find the minimum value of (sec^(-1)x)^2+("c o s e c"^(-1)x)^2

Find the maximum value of 4sin^2x+3cos^2x+sin(x/2)+cos(x/2)dot

Find the minimum value of the function f(x)=(pi^2)/(16cot^(-1)(-x))-cot^(-1)x

Find the greatest value of f(x)1/(2a x-x^2-5a^2)in[-3,5] depending upon the parameter adot

For 2 lt x lt 4 find the values of |x|. (ii) For -3 le x le -1 , find the values of |x|. (iii) For -3 le x lt 1, find the values of |x| (iv) For -5 lt x lt 7 find the values of |x-2| (v) For 1 le x le 5 find fthe values of |2x -7|