If length of perpendicular drawn from points of a curve to a straight line approaches zero along an infinite branch of the curve, the line is said to be an asymptote to the curve. For example , y-axis is an asymptote to `y = lnx`& x-axis is an asymptote to ` y = e^(-x)`. If `lim_(xrarr0) f(x) = e` (a finite number) then `y = e` is an asymptote to `y = f(x)` . Similarly if `lim_(xrarr0)f(x) = alpha`, then `y = alpha` is also an asymptote. If `lim_(xrarra)f(x) = oo` or `lim_(xrarra) f(x) = -oo`, then `x = a` is a an asymptote to `y = f(x)`. Number of asymptotes parallel to co -ordinate aces for the function `f(x) = ((x+1)(x+2))/((x-1)(x-2))` is equal to :A. 1B. 2C. 3D. 4

If length of perpendicular drawn from points of a curve to a straight

1.	If length of perpendicular drawn from points of a curve to a straight line approaches zero along an infinite branch of the curve, the line is said to be an asymptote to the curve. For example , y-axis is an asymptote to `y = lnx`& x-axis is an asymptote to ` y = e^(-x)`. If `lim_(xrarr0) f(x) = e` (a finite number) then `y = e` is an asymptote to `y = f(x)` . Similarly if `lim_(xrarr0)f(x) = alpha`, then `y = alpha` is also an asymptote. If `lim_(xrarra)f(x) = oo` or `lim_(xrarra) f(x) = -oo`, then `x = a` is a an asymptote to `y = f(x)`. Number of asymptotes parallel to co -ordinate aces for the function `f(x) = ((x+1)(x+2))/((x-1)(x-2))` is equal to :A. 1B. 2C. 3D. 4
Answer» Correct Answer - C

Consider the integral `I=int_(0)^(2pi)(dx)/(5-2cosx)` Making the substitution `"tan"1/2x=t`, we have `I=int_(0)^(2pi)(dx)/(5-2cosx)=int_(0)^(0)(2dt)/((1+t^(2))[5-2(1-t^(2))//(1+t^(2))])=0` The result is obviously wrong, since the integrand is positive and consequently the integral of this function cannot be equal to zero. Find the mistake.
The area bounded by the curves `y=cosx` and `y=sinx` between the ordinates `x=0` and `x=(3pi)/2` isA. `4sqrt(2) + 2`B. `4sqrt(2) +1`C. `4sqrt(2) + 1`D. `4sqrt(2) - 2`
Obtain the area enclosed by region bounded by the curves `y = x ln x` and ` y = 2x-2x^(2)`.A. `7//6`B. `7//24`C. `12//7`D. `7//12`
If `I_n=int_0^pi e^x(sinx)^n dx ,` then `(I_3)/(I_1)` is equal toA. `3//5`B. `1//5`C. `1`D. `2//5`
Prove that:`I_n=int_0^oox^(2n+1)e^-x^2dx=(n !)/2,n in Ndot`
If f(x) is continuous and `int_(0)^(9)f(x)dx=4`, then the value of the integral `int_(0)^(3)x.f(x^(2))dx` isA. 2B. 18C. 16D. 4
`lim_(trarr0) int_(0)^(2pi)(|sin(x+t)-sinx|)/(|t|)dx` equalsA. 2B. 4C. 43469D. 1
Given that `lim_(nrarroo) sum_(r=1)^(n) (log_(e)(n^(2)+r^(2))-2log_(e)n)/n = log_(e)2+pi/2-2`, then evaluate : ` lim_(nrarroo) (1)/(n^(2m))[(n^(2)+1^(2))^(m)(n^(2)+2^(2))^(m) "......"(2n^(2))^(m)]^(1//n)`.
`lim_(nrarroo) sum_(r=0)^(n-1) (1)/(sqrt(n^(2)-r^(2)))`
`lim_(nrarroo) (((n+1)(n+2)"........"3n)/(n^(2n)))^(1//n)` is equal to :A. `(27)/(e^(2))`B. `(9)/(e^(2))`C. `3 log3-2`D. `(18)/(e^(4))`