Home
Class 12
MATHS
Match the following lists (where [x] rep...

Match the following lists (where `[x]` represents the greatest integer function) and then choose the correct code.

Codes :
`{:(,"a b c d"),((1),"s r q p"),((2),"q p s p"),((3), "s r p q"),((4),"p p q r"):}`

Text Solution

Verified by Experts

The correct Answer is:
`(2)`
a. `underset(xto0)lims(-1)^([1//x])`
`L.H.L.=underset(hto0)lim(0-h)(-1)^([(1)/(0-h)])=0`
`R.H.L.=underset(hto0)lim(0+h)(-1)^([(1)/(0+h)])=0`
b. `underset(xto2)lim(-1)^([x])`
`L.H.L.=underset(hto0)lim(-1)^([2-h])=(-1)^(1)=-1`
`R.H.L.=underset(hto0)lim(-1)^([2+h])=(-1)^(2)=1`
So limit does not exist.
c.`underset(xto(3)/(2))lim(x-[x])`
`L.H.L.=underset(hto0)lim(3)/(2)-h-[(3)/(2)-h]=underset(hto0)lim(3)/(2)-h-1=(1)/(2)`
`R.H.L.=underset(hto0)lim(3)/(2)+h-[(3)/(2)+h]=underset(hto0)lim(3)/(2)+h-1=(1)/(2)`
`L.H.L.=R.H.L.=(1)/(2)`
`underset(xto0)lim[x]((e^(1//x)-1)/(e^(1//x)+1))`
`L.H.L.=underset(hto0)lim[0-h](((1)/(e^(0-h)-1))/((1)/(e^(0-h)+1)))`
`=underset(hto0)lim[-h]((e^(-(1)/(h))-1)/((1)/(e^(0-h)+1)))=(-1)xx(-1)=1`
R.H.L.`=underset(hto0)lim[0+h]((e^((1)/(h))-1)/(e^((1)/(h)+1)))=0`
Limit does not exist
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE PUBLICATION|Exercise Numerical Value Type|26 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Archives JEE MAIN|8 Videos

  • LIMITS

    CENGAGE PUBLICATION|Exercise Linked Comprehension Type|20 Videos

  • JEE 2019

    CENGAGE PUBLICATION|Exercise Chapter 10|8 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE PUBLICATION|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Consider a DeltaABC in which sides AB and AC are perpendicular to x-y-4=0 and 2x-y-5=0, repectively. Vertex A is (-2, 3) and the circumcenter of DeltaABC is (3/2, 5/2). The equation of the line in List I is of the form ax+by+c=0, where a,b,c in I. Match it with the corresponding value of c in list II and then choose the correct code. Codes : {:(a, b, c, d),(r, s, p, q),(s, r, q, p),(q, p, s, r),(r, p, s, q):}

Consider int(x^(3)+3x^(2)+2x+1)/(sqrt(x^(2)+x+1))dx =(ax^(2)+bx+c)sqrt(x^(2)+x+1)+lambda int(dx)/(sqrt(x^(2)+x+1)) Now, match the following lists and then choose the correct code. Codes: {:(,a,b,c,d),((1),q,p,s,r),((2),s,p,q,r),((3),r,q,p,s),((4),q,s,p,r):}

Simplify the following: (6p-4q+2r) + (2p+3q-4r)

Find the angle between the lines whose direction ratios are p, q, r and q-r, r-p, p-q

If p+q+r=0=a+b+c , then the value of the determinant |[p a, q b, r c],[ q c ,r a, p b],[ r b, p c, q a]|i s (a) 0 (b) p a+q b+r c (c) 1 (d) none of these

Construct the truth table for the followings statements : (a) (p^^q) to ~ p " " (b) (p^^q) to (pvvq) (c) (p^^q) to r " " (d) [p^^(~r)] to (qvvr)

If the inverse of implication p to q is defined as ~ p to ~q , then the inverse of the proposition ( p ^^ ~ q) to r is

If r,s,t are prime numbers and p,q are the positive integers such that LCM of p,q is r^2t^4s^2 , then find the number of ordered pair (p,q).

If the pth, qth, and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is a. (p r)/(q^2) b. r/p c. (q+r)/(p+q) d. (q-r)/(p-q)

If A={p,q,r} and B={q,p,r}. Then check whether A=B or not.