If alpha and beta are the roots of the q...

If `alpha` and `beta` are the roots of the quadratic equation `ax^2 + bx + c = 0` , then evaluate `lim_(x->1/alpha)sqrt{(1-cos(cx^2 + bx + a))/(2(1- alphax)^2)}`

A

c(a-b)

B

`c/(2alpha)(1/alpha-1/beta)`

C

`1/beta(1/alpha-1/beta)`

D

`|(1/alpha-1/beta)c/(2alpha)|`

Text Solution

Verified by Experts

The correct Answer is:

D

Promotional Banner

Promotional Banner

Topper's Solved these Questions

LIMITS AND CONTINUITY
MCGROW HILL PUBLICATION|Exercise Exercise (Numerical Answer)|16 Videos
LIMITS AND CONTINUITY
MCGROW HILL PUBLICATION|Exercise Questions for Previous Years AIEEE/JEE Main Papers|44 Videos
LIMITS AND CONTINUITY
MCGROW HILL PUBLICATION|Exercise Exercise (Level 1 Single Correct Answer)|39 Videos
JEE (MAIN) QUESTIONS WITH SOLUTIONS MATHEMATICS (7 TH JAN-MORNING )
MCGROW HILL PUBLICATION|Exercise QUESTIONS|25 Videos
MATHEMATICAL INDUCTION AND BINOMIAL THEOREM
MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|20 Videos

Similar Questions

Explore conceptually related problems

If alpha and beta are the roots of the quadratic equation ax^(2)+bx+c=0, then evaluate lim_(x rarr(1)/(a))sqrt((1-cos(cx^(2)+bx+a))/(2(1-alpha x)^(2)))

If alpha,beta are the roots of the quadratic equation ax^(2)+bx+c=0 then alpha beta =

If alpha and beta are roots of the equation ax ^(2) + bx + c, then find the value of the (1)/(alpha) + (1)/(beta).

If alpha and beta are the roots of the equation ax^(2) + bx + c = 0 , then what is the value of the expression (alpha + 1)(beta + 1) ?

If alpha , beta are the roots of the quadratic equation ax^(2) + bx + c = 0 , then the quadratic equation whose roots are alpha^(3) , beta^(3) is

If alpha and beta are the roots of the equation x^(2) + bx + c = 0 , then the roots of the equation cx^(2) -b x + 1=0 are

If alphaandbeta are the roots of the equation ax^(2)+bx+c=0 , then an equation whose roots are (1)/(alpha)and(1)/(beta) is

If alpha and beta are roots of the equation ax^2+bx +c=0 , then lim_(xrarralpha) (1+ax^2+bx+c)^(1//x-alpha) , is

MCGROW HILL PUBLICATION-LIMITS AND CONTINUITY-Exercise (Level 2 Single Correct Answer)

If alpha and beta are the roots of the quadratic equation ax^2 + bx + ...
Text Solution
|
Let f be a continuous function satisfying f(x) f(y)=f(x)+f(y)+f(xy)-2 ...
Text Solution
|
The value of lim(x to oo)(e^(1//x)-e^(-1//x))/(e^(1//x)+e^(-1//x)) tan...
Text Solution
|
Let f be a continuous function satisfying f(x+y)=f(x)+f(y) for all x,y...
Text Solution
|
Let f(x)=e^x sgn (x+[x]) , where sgn is the signum function and [x] is...
Text Solution
|
The value of lim(x-> -4) (tanpix)/(x+4) + lim(x->oo)(1+1/x^2)^x is
Text Solution
|
The value of lim(x to 0) ("sinx"/x)^("sin x"/"x-sinx") is
Text Solution
|
The value of lim(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7...
Text Solution
|
Let f(x)=x-1 and g(x)=1/x. Then the set of points where gofog is conti...
Text Solution
|
Let f(x)=lim( n to oo) ([x^2]+[(2x)^2]+... + [(nx)^2])/n^3 then the se...
Text Solution
|
If : f(x){:( =1", ... x is rational"),(=0", ...x is irr...
Text Solution
|
Let f(x) be given that f(x)={{:(,x,"if x is rational"),(,1-x,"if x is ...
Text Solution
|
Let f:R to R be any function. Defining g: R to R by g(x)=|f(x)|" for "...
Text Solution
|
Let f be a function defined on R by f(x)=lim(n to oo) (log (3+x)-x^(2n...
Text Solution
|
If f(x)=((x^2+5x+3)/(x^2+x+2))^x then lim(xtooo)f(x) is equal to
Text Solution
|
Let f(x) be defined for all > x0 and be continuous. Let f(x) satisfies...
Text Solution
|
Given the function f(x)=1/(1-x), the numbers of discontinuities of f^...
Text Solution
|
If f(x)=(1+sinx-cosx)/(1-sinx-cosx), x ne 0 . The value of f(0) so tha...
Text Solution
|
If f(x)={(ax+1",", x le (pi)/(2)),(sinx+b",", x gt (pi)/(2)):} is cont...
Text Solution
|
If f(x)={((x^(3)+x^(2)-16x+20)/((x-2)^(2))",",x ne 2),(k",", x =2):} ...
Text Solution
|