If `lim_(x→0) ` ​ `(x^asin^b x)/(sin(x^c))`, where a , b , c in R ~{0},exists and has non-zero value. Then, `

lim_(xto0) (x^(a)sin^(b)x)/(sin(x^(c))) , where a,b,c inR~{0}, exists and has non-zero value. Then,

("lim")_(xvec0)(x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then, a+c = (a) b (b) -1 0 (d) none of these

lim_(x->0)(1+(asinb x)/(cosx))^(1/x), where a,b are non zero constants is equal to :

The value of lim_(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)0 (b) -1 (c) 1 (d) 2

The value of lim_(xrarr0) (a^x-b^x)/(x) ,is

The value of lim_(x->oo)(a x^2+b x+c)/(dx+e)(a , b , c , d , e in R-{0}) depends on the sign of :

If lim_(xrarr0)(ae^x-b cos x + ce^(-x))/(xsinx )=2 ,then a+b+c=

lim_(x to 0) (1+ax)^(b/x) =e^(2) , " where" a, b in N such that a+ b = 3 , then the value of (a,b) is

If lim_(xrarr0)(sin2x-asinx)/(x^(3)) exists finitely, then the value of a is

(lim)_(x->oo)(sinx)/x equals a. 1 b . 0 c. oo d. does not exist