Limits and Derivatives

For , , R, if x 0 x2 x + ( - 1)ex2 2x - x = 3, then + - is equal to :

1. -1
2. 4
3. 6
4. 7

If x 0 (2x) + a (4x) - bx4 is finite, then (a + b) is equal to:

1. 0
2. 34
3. -1
4. 12

Let [t] be the greatest integer less than or equal to t. Then the least value of p N for which x 0+ (x ( [ 1x ] + [ 2x ] + + [ px ] ) - x2 ( [ 1x2 ] + [ 22x2 ] + + [ 92x2 ] ) ) 1 is equal to .

Let f(x) = n r=0n ( (x/2r+1 ) + 3 (x/2r+1 )1 - 2 (x/2r+1 ) ). Then x 0 ex - ef(x)(x - f(x)) is equal to .

x 0 cosecx ( 2 2x+3 x- 2x+ x+4 ) is

1. 1 15
2. 12 5
3. 0
4. - 12 5

x (2x2-3x+5 )(3x-1) x2 (3x2+5x+4 ) (3x+2)x is equal to :

1. 2e3
2. 23 e
3. 2e 3
4. 2 3e

If x ( ( e1-e ) ( 1e- x1+x ) )x= , then the value of e 1+ e equals :

1. e-2
2. e2
3. e
4. e-1

x 0 e - (1 + 2x) 12xx is equal to

1. -2e
2. e - e2
3. 0
4. e

The value of x 0 2 ( 1 - x 2x [3] 3x [10] 10xx2 ) is .

If = x 0+ ( e x - e x x - x ) and = x 0(1 + x) 12 x are the roots of the quadratic equation ax2 + bx - e = 0, then 12 e(a + b) is equal to .