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The value of `lim_(x->0) 1/x int_(x^3)^x ((1+t)^(1/3)-1)/t`dt is equal to

Let `f :R -> R` be a function such that for some `p >0, f (x+ p) =(f(x)-5)/(f(x)-3)` for all x `in`R . Then period of f is

The value of `lim_(x->0)[x^2/(sin x. tan x)]`(Where [.] denotes greatest integer function) is

`f(x)= {(x^2/4-(3x)/2+13/4, text(for) x<1),(|x-3|, text(for) x>=0):}` then `lim_(x->1) f(x)`

`lim_(n->oo) (1+1/(n^2+cos n))^(n^2+n)` equals

Suppose that the function f, g, f’, and g’ are continuous over [0,1] , g(x) `!=0` for x `in` [0,1],f(0)=0,g(0)`=pi`, f(1)=`2015/2` , g(1) =1.The value of

`int_0^1 (f(x)g'(x)(g^2(x)-1)+f'(x).g(x)(g^2(x)+1))/(g^2(x)) dx` is equal to

`Let a=lim_(x->0)((ln(cos 2x))/(3x^2)) , b = lim_(x->0)((sin^2 2x)/(x(1-e^x))) ,c=lim_(x->1) ((sqrtx-x)/(ln x)) then`

Let `a_0`=1, `a_1=2` and for `n>=1, n(n+1)a_(n+1)=n(n-1)a_n-(n-2)a_(n-1), then lim_(n->oo)(a_n)=`

Let `f : A -> B = [0,oo)` be a function defined by f (x)= |x|, then

Let `A=[-2,-1]uu[1,2]`, If `f:A->R` is defined by`f(x)=x^3`, Then

Let `f: [0, 2]->R` be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0)=1. Let `F(x)= int_0^(x^2) f(sqrtt)dt`

for x `in` [0,2]. If F'(x)=f'(x) for all x `in` (0,2), then F(2) equals

If `f (x) =lim_(n->oo) (X^(2n)-1)/(X^(2n)+1)`, then which of the following is correct

Let f and g be differentiable functions satisfyin `g^1`(a) = 2, g(a) = b and fog = I (identity function) then`f^1` (b) =

Let `f: [a, b] -> [1,oo)`, be a continuous function and let `g: R -> R` be defined as

`g(x)={(0,if x<a),(int_a^x f(t)dt ,if a<=x<=b),(int_a^bf(t)dt ,if x>b):}`.

Then

Let f(x) be a function for all x `in` R and f'(0) = 1 then g(x)= f (lxl)-`sqrt((1-cos2x)/2)`

Let f :`(- pi/2, pi/2) ->` R be given by

`f(x) = (log(sec x + tan x))^3`

Then which of the following is wrong?

For every pair of continuous functions `f, g : [0, 1] -> R` such that max.`{f(x):x in [0,1]}=max.{g(x):x in [0,1]}`,

The correct statement(s) is (are)

`g(x)` is the inverse function of `f(x)` and `f'(x) = cos 2x`, then `g'(x)` is equal to

Let `(x, y)` be a variable point on the curve `4x^2 + 9y^2 – 8x – 36y + 15 = 0` then min `(x^2 – 2x + y^2 – 4y + 5) + max (x^2 – 2x + y^2 – 4y + 5)`

Consider the function `f(x) =8x^2 -7x+ 5` on the interval `[-6,6]` . The value of c that satisfies the condition of the Lagrange's mean value theorem, is

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