`("lim")_(xvec0)((1+5x^2)/(1+3x^2))^1//x^2=____`

f(x) is polynomial function of degree 6, which satisfies ("lim")_(xvec0)(1+(f(x))/(x^3))^(1/x)=e^2 and has local maximum at x=1 and local minimum at x=0a n dx=2. Column I, Column II The coefficient of x^6 , p. 0 The coefficient of x^5 , q. 2 The coefficient of x^4 , r. -(12)/5 The coefficient of x^3 , s. 2/3

Evaluate: ("lim")_(xvec0)1/xsin^(-1)((2x)/(1+x^2))

Evaluate: ("lim")_(xvec0)(1-cos2x)/(x^2)

("lim")_(xvec0)1/xcos^(-1)((1-x^2)/(1+x^2)) is equal to (a)1 (b) 0 (c) 2 (d) none of these

If ("lim")_(xvec0)[1+x+(f(x))/x]^(1/x)=e^3, then find the value of 1n(("lim")_(xvec0)[1+(f(x))/x]^(1/x))i s____

Evaluate: ("lim")_(xvec0)(1^(1//sin^(2)x)+2^(1/(sin^(2)x)+....+n^(1//sin^(2)x)))^(sin^(2)x)

("lim")_(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c) 1 (d) -1

Find ("lim")_(xvec0){tan(pi/4+x)}^(1//x)

Evaluate: ("lim")_(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

Evaluate : ("lim")_(xvec1)(2/(1-x^2)+1/(x-1))