" 1."[343^(" cर ")(x+4)(x+10)],[" (i) "(x+4)]

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

int(x^(4))/(1+x^(10))dx

Factorize (i) (x^4+4) (ii) (x^2+(4)/(x^2)) (iii) (x^4+(1)/(x^4)+1)

If (x - 1/x) = 4 , find the value of (i) (x^(2) - 1/(x^(2))) , (ii) (x^(4) + 1/(x^(4))).

lim_ (x rarr oo) ((x + 2) ^ (10) + (x + 4) ^ (10) ++ (x + 20) ^ (10)) / (x ^ (10) +1) =

a.) 2 ^ (2x + 2) = 4 ^ (2x-1) b.) 7 ^ (x) = 343

If i= sqrt(-1) , prove that following (x+1+ i) (x + 1- i) (x-1 + i) (x-1-i)= x^(4) + 4

If i= (sqrt-1) , prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)= x^(4) + 4

If 4^(1+x)+4^(1-x)=10 , find x.