" 4) "(214)/(114)(4)^(2x-1)-(16)^(x-1)=384^((1)/(21))x^(sqrt(116))cos^(2)5

(1)/(sqrt(21+4x-x^(2)))

Show that (16(32^(x))-2^(3x-2)*4^(x+1))/(15*2^(x-1)*16^(x))-(5*5^(x-1))/(sqrt(5^(2x))) is given

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)

If (4)^(2x- 1) - (16)^(x-1) = 384. find the value of x .

Find the integral int(1)/(5-8x-x^(2))dx A. (1)/(2sqrt(21))log|(sqrt(21)+(x+4))/(sqrt(21)-(x+4))|+C .B. (1)/(2sqrt(21))log|(sqrt(21)-(x+4))/(sqrt(21)+(x+4))|+C C. (1)/(sqrt(21))log|((x+4)+sqrt(21))/((x+4)-sqrt(21))|+Cquad D. (1)/(sqrt(21))log|((x+4)-sqrt(21))/((x+4)+sqrt(21))|+C

cos^(-1)((x^(2))/(6)+sqrt(1-(x^(2))/(9))sqrt(1-(x^(2))/(4)))=cos^(-1)((x)/(3))-cos^(-1)((x)/(2)) hold for all x belonging to

lim_(x rarr(1)/(sqrt(2)^(+)))(cos^(-1)(2x sqrt(1-x^(2))))/((x-(1)/(sqrt(2))))-lim_(x rarr(1)/(sqrt(2)^(-)))(cos^(-1)(2x sqrt(1-x^(2))))/((x-(1)/(sqrt(2))))

lim _(x to ((1)/(sqrt2))^(+))(cos ^(-1) (2x sqrt(1- x ^(2))))/((x-(1)/(sqrt2)))- lim _(x to ((1)/(sqrt2))^(-))(cos ^(-1) (2x sqrt(1-x ^(2))))/((x- (1)/(sqrt2)))=