lom n:(x-2)^(4)(x-3)^(3)(x-4)^(2)(1-x)<=0

(lim)_(xvecoo)(2. x^(1//2)+3. x^(1//3)+4. x^(1//4)++ndotx^(1//n))/((3x-4)^(1//2)+(3x-4)^(1-3)+(3x-4^)^(1//3)++(3x-4)^(1//n)) (here n in N ,ngeq2 ) is equal to 1 dot2/(sqrt(3)) 2. (sqrt(3))/2 3. 1/2 4. 1/(sqrt(3)) 5. 2

Solve for :x:(x-1)/(x-2)+(x-3)/(x-4)=3(1)/(3),x!=2,4

Solve for x:(x-1)/(x-2)+(x-3)/(x-4)=3(1)/(3);x!=2,4

((x-1)/(x-2))-((x-2)/(x-3))=((x-3)/(x-4))-((x-4)/(x-5))

Find the coefficient of x^(r) in the expansion of (x+4)^(n)+(x+4)^(n-1)(x+3)+(x+4)^(n-2)(x+3)^(2)+.....+(x+3)^(n)

Coefficient of x(n^(2)+n-14)/(2) in,(x-1)(x^(2)-2)(x^(3)-3)(x^(4)-4)......(x^(n)-n),(n>=8) is

Solve : 2^(4x)*4^(3x-1)=(4^(2x))/(2^(3x)) .

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

If Delta (x) =|{:(4x-4,(x-2)^(2),x^(3)),(8x-4sqrt(2),(x-2sqrt(2)^(2)),(x+1)^(3)),(12x-4sqrt(3),(x-2sqrt(3))^(2),(x-1)^(3)):}| then

Observe the following pattern (1x2)+(2x3)=(2x3x4)/(3)(1x2)+(2x3)+(3x4)=(3x4x5)/(3)(1x2)+(2x3)+(3x4)+(4x5)=(4x5x6)/(3) and find the of (1x2)+(2x3)+(3x4)+(4x5)+(5x6)