(d) (c) -1 (d) 56. lim VT - V cos x -1 $x+

Which of the following is/are true? (a) lim_(x rarr oo)((2+x)^(40)(4+x)^(5))/((2-x)^(45))=1(b)lim_(x rarr0)(1-cos^(3)x)/(x sin x cos x)=(3)/(2)(c)lim_(x rarr0)(ln(1+2x)-2ln(1+x))/(cot^(-1)(sqrt(x+1)-sqrt(x)))=-1 (d) lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^(1)((2x+1)/((x-1)^(2)))=1)=-1 (d)

(lim)_(xvec0)(1-cos^3x)/(x s i n x cos x) is equal to 3 b. 1/2 c. 3/2 d. -3/2

Which of the following limits does not exist ?(a) lim_(x->oo) cosec^(-1) (x/(x+7) (B) lim_(x->1) sec^(-1) (sin^(-1)x) (C) lim_(x->0^+) x^(1/x) (D) lim_(x->0) (tan(pi/8+x))^(cotx)

(lim_(x rarr))_(xvec 0)(1-cos^(3)x)/(x sin x cos x) is equal to 3 b.(1)/(2) c.(3)/(2) d.-(3)/(2)

If x satisfies the cubic equation ax^(3)+bx^(2)+cx+d=0 such that cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)=pi , then find the value of (b+c)-(a+d) .

If x satisfies the cubic equation ax^(3)+bx^(2)+cx+d=0 such that cos^(-1)(x)+cos^(-1)(2x)+cos^(-1)(3x)=pi , then find the value of (b+c)-(a+d) .

(d)/(dx) {Cos ^(-1) ""(x-x ^(-1))/(x + x ^(-1))}=

lim_(x rarr 0)(1-cos x)/(x log(1+x)) (a) \ \ \ 1 (b) \ \ \ 0 (c) -1 (d) \ \ \ 1/2

The (lim)_(x->0)(cos x)^(cotx) is -1 b. 1 c. 0 d. none of these

(lim)_(x rarr)(sin^(4)x-sin^(2)x+1)/(cos^(4)x-cos^(2)x+1) is equal to (a) 0( b) 1 (c) (1)/(3)(d)(1)/(2)