Let f(x)= `[[cos x, -sin x, 0],[sin x, cos x, 0],[0,0,1]]` ,Show that `f (x) f(y)= f(x+y)`.

If f(x)=[[cos x,-sin x,0],[sin x,cos x,0],[0,0,1]] , show that f(x).f(y)=f(x+y)

If F (x) = [[cos x,-sin x,0],[sin x, cos x, 0],[0,0,1], then show that F(x) F(y)= F (x+y).

Inverse of f(x) = [(cos x , sin x, 0),(-sin x, cos x, 0),(0,0,1)] is

Let f(x) = |{:(2cos ^(2) x,,sin 2x,,-sin x),(sin 2x,,2 sin^(2)x,,cos x),(sin x,,-cos x,,0):}| .then the value of int_(0)^(pi//2) [ f(x) +f'(x) ] dx " is "

Let f(x) = {:{((sinx)/x + cosx, when x ne 0),(2, when x = 0):} show that f (x) is continouous at x = 0.

If f(x) = |(sin x, cos x , tan x),(x^3, x^2 ,x),(2x, 1,x)| then Lim_(x to 0) (f(x))/(x^2) equals

Let f(x) = |x| cos (1/x) for x ne 0 . Write the down the value of (f) (0) if f is continuous at x = 0

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is a. ((12)/(25),(-9)/(25)) b. ((12)/(25),(9)/(25)) c. ((16)/(25),(-8)/(25)) d. ((24)/(25),(-7)/(25))

A function y-f (x) satisfies the differential equation f (x) sin 2x - cos x+(1+ sin ^(2)x) f'(x) =0 with f (0) =0. The value of f ((pi)/(6)) equals to :

Let f(x) = (x - a) cos (1/(x-a)) for x ne a and le f (a) = 0. Show that f is continuous at x = a but not derivable thereat.