Prove that 4-32 is an iontional

prove that f(x) is a continuous funcation where f(x) {{:( (x^(4)-16)/(x-2)",", if , xne 2),( 32 ",", if , x =2):}

Prove that 3^(2n)+24n-1 is divisible by 32 .

Prove that 3^(2n)+24n-1 is divisible by 32 .

Prove that 3^(2n)+24n-1 is divisible by 32 .

Prove that if the co-ordinates of A and B be (3,2) and (-6,-4) respectively, then the line AB passes through the origin.

Prove that : 2 tan^-1(1/5) + tan^-1(1/4) = tan^-1(32/43)

Consider the points A (3,2,-4), B (5,4,-6) and C (9,8,-10) Using section formula, prove that A, B, C are collinear.

Prove that A+A^T is symmetric and A-A^T is skew symmetric matrix, where A=[[1,2,4],[3,2,1],[-2,-3,2]]

Write (33)! = [32.16.8.4.2]. [33.31.30…3.1] Hence, prove that (33)! is divisible by 2^15

Prove that x=2 and x=3 are roots of the equation :det[[x-5,32,x]]=0