Home
Class 12
MATHS
If f(x) + f(y) = f(xy-sqrt(1-x^(2))sqrt(...

If `f(x) + f(y) = f(xy-sqrt(1-x^(2))sqrt(1-y^(2))), f(0) = (pi)/(2)` and f is differentiable in (-1, 1).
Then `|lim_(x rarr 0)(2f(x)-pi)/(x)|=`

Text Solution

Verified by Experts

The correct Answer is:
2
Here `f(x) = cos^(-1)x`
Now `lim_(x rarr 0)(2cos^(-1) x-pi)/(x) ((0)/(0))` form LH Rule
`rArr lim_(r rarr 0)(-2)/(sqrt(1-x^(2))) = -2 rArr |lim_(x rarr 0)(2f(x)-pi)/(x)|= +2`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MOCK TEST 3

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION-2)|10 Videos

  • MOCK TEST 2

    VMC MODULES ENGLISH|Exercise PART III : MATHEMATICS (SECTION - 2)|10 Videos

  • MOCK TEST 4

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

Similar Questions

Explore conceptually related problems

If f(x)=sqrt(x^(2)-2x+1), then f' (x) ?

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is

f(x)=sqrt(1-sqrt(1-x^2) then at x=0 ,value of f(x) is

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,yinR,f(x) is differentiable and f'(0)=1. Range of y=log_(3//4)(f(x)) is

If f(x) =x + int_(0)^(1) (xy^(2)+x^(2)y)(f(y)) dy, "find" f(x) if x and y are independent.

Let (f(x+y)-f(x))/(2)=(f(y)-1)/(2)+xy , for all x,yinR,f(x) is differentiable and f'(0)=1. Domain of log(f(x)), is

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

if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

if f'(x)=sqrt(2x^2-1) and y=f(x^2) then (dy)/(dx) at x=1 is:

Let f(x)+f(y)=f(xsqrt(1-y^2)+ysqrt(1-x^2))[f(x) is not identically zero]. Then f(4x^3-3x)+3f(x)=0 f(4x^3-3x)=3f(x) f(2xsqrt(1-x^2)+2f(x)=0 f(2xsqrt(1-x^2)=2f(x)

Home
Profile