" (b) "(3)/(2)u^(3)-1+5u^(4)+3u-sqrt(2)u^(2)

Find the point of discontinuity of y=f(u) where f(u)=(3)/(2u^(2)+5u-3) and u=(1)/(x+2)

int_(2)^(3)u sqrt(5-u)du

Let U_(1)=1,U_(2)=1 and U_(n+2)=U_(n+1)+U_(n) for n>=1. Use mathematical induction to such that: :U_(n)=(1)/(sqrt(5)){((1+sqrt(5))/(2))^(n)-((1-sqrt(5))/(2))^(n)} for all n>1

Let u_(n)=(1)/(sqrt((5)))[((1+sqrt(5))/(2))^(n)-((1-sqrt(5))/(2))^(n)] (0=0,1,2,3,……) , prove that u_(n+1)=u_(n)+u_(n-1)(n ge 1) .

Let u_(1)=1,u_2=2,u_(3)=(7)/(2)and u_(n+3)=3u_(n+2)-((3)/(2))u_(n+1)-u_(n) . Use the principle of mathematical induction to show that u_(n)=(1)/(3)[2^(n)+((1+sqrt(3))/(2))^n+((1-sqrt(3))/(2))^n]forall n ge 1 .

Let u_(1)=1,u_2=2,u_(3)=(7)/(2)and u_(n+3)=3u_(n+2)-((3)/(2))u_(n+1)-u_(n) . Use the principle of mathematical induction to show that u_(n)=(1)/(3)[2^(n)+((1+sqrt(3))/(2))^n+((1-sqrt(3))/(2))^n]forall n ge 1 .

Let u_(1)=1,u_2=2,u_(3)=(7)/(2)and u_(n+3)=3u_(n+2)-((3)/(2))u_(n+1)-u_(n) . Use the principle of mathematical induction to show that u_(n)=(1)/(3)[2^(n)+((1+sqrt(3))/(2))^n+((1-sqrt(3))/(2))^n]forall n ge 1 .

Let u_(1)=1,u_2=2,u_(3)=(7)/(2)and u_(n+3)=3u_(n+2)-((3)/(2))u_(n+1)-u_(n) . Use the principle of mathematical induction to show that u_(n)=(1)/(3)[2^(n)+((1+sqrt(3))/(2))^n+((1-sqrt(3))/(2))^n]forall n ge 1 .

int_(1)^(2)((x^(2)-1)dx)/(x^(3)*sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where u are ( in their blowest form.Find the value of )/(sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where of ((1000)u)/(v)

If u_(1) =sqrt2, u_(2) =sqrt(2sqrt(2)), u_(3) =sqrt(2sqrt(2sqrt2)),... then the value of u_(10):u_(9) is-