If `x_1 and x_2` are the real and distinct roots of `a x^2+b x+c=0,` then prove that `lim_(n->x_1){1+"sin"(a x^2+b x+c)}^(1/(x-x_1))=e^(a(x_1-x_2))`

If x_1 and x_2 are two distinct roots of the equation a cosx + b sinx =c then tan""(x_1 + x_2)/(2) is equal to :

If alpha,beta are the distinct roots of x^(2)+bx+c=0 , then lim_(x to beta)(e^(2(x^(2)+bx+c))-1-2(x^(2)+bx+c))/((x-beta)^(2)) is equal to

If x_(1) and x_(2) are two distinct roots of the equation a cos x+b sin x=c, then tan((x_(1)+x_(2))/(2)) is equal to (a)(a)/(b) (b) (b)/(a) (c) (c)/(a) (d) (a)/(c)

lim_(x rarr0)((1)/(x sin^(-1)x)-(1-x^(2))/(x^(2)))

x_(1) and x_(2) are the roots of ax^(2)+bx+c=0 and x_(1)x_(2)<0. Roots of x_(1)(x-x_(2))^(2)+x_(2)(x-x_(1))^(2)=0 are a.real and of opposite sign b.negative c.positive d. none real

The value of lim_(x rarr0)((1+x)^((1)/(x))-e+(1)/(2)ex)/(x^(2)) is

lim_(x rarr0)(e^(x)-1-sin x-(tan^(2)x)/(2))/(x^(3))

lim_(x rarr1)(a sin(x-1)+b cos(x-1)+4)/(x^(2)-1)=-2, then |a+b|

(lim)_(x->0)((1-t a n x)/(1+sin x))^(cos e c\ x)

If underset(x to 1)lim (ax^(2)+bx+c)/((x-1)^(2))=2" then "underset(x to 1)lim ((x-a)(x-b)(x-c))/((x+1))=