Home
Class 12
MATHS
The value of p and q for which the funct...

The value of p and q for which the function `f(x)""={(sin(p+1)x+sinx)/x , x<0q , x=0(sqrt(x+x^2)-sqrt(x))/(x^(3//2)), x >0}` is continuous for all x in R, are: (1) `p=1/2, q=-3/2` (2) `p=5/2, q=-1/2` (3) `p=-3/2, q=1/2` (4) `p=1/2, q=3/2`

Text Solution

Verified by Experts

The correct Answer is:
3
`lim_(n to0)f(0-h) =1+(p+1)=p+2`
`lim_(n to 0) f(0+h) =1/2`
`f(0)=q`
`p+2 =q` and `q=1/2`
`(-3/2, 1/2)`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST -14

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE MAIN REVISION TEST - 7|JEE - 2020

    VMC MODULES ENGLISH|Exercise Mathematics (Section - 2) Numercial type questions|5 Videos

  • JEE MAIN REVISION TEST -17 (2020)

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

The value of p and q for which the function f(x)""={(sin(p+1)x+sinx)/x , x 0} is continuous for all x in R, are: (1) p=1/2, q=-3/2 (2) p=5/2, q=-1/2 (3) p=-3/2, q=1/2 (4) p=1/2, q=3/2

If p and q are the roots of the equation x^2-p x+q=0 , then (a) p=1,\ q=-2 (b) p=1,\ q=0 (c) p=-2,\ q=0 (d) p=-2,\ q=1

The parabola y=x^2+p x+q cuts the straight line y=2x-3 at a point with abscissa 1. Then the value of pa n dq for which the distance between the vertex of the parabola and the x-axis is the minimum is (a) p=-1,q=-1 (b) p=-2,q=0 (c) p=0,q=-2 (d) p=3/2,q=-1/2

The value of p and q(p!=0,q!=0) for which p ,q are the roots of the equation x^2+p x+q=0 are (a) p=1,q=-2 (b) p=-1,q=-2 (c) p=-1,q=2 (d) p=1,q=2

If range of the function f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1) is [p ,q], then the value of 3 p+6q+1 is (a) (10)/3 (b) 7/3 (c) 28 (d) None of these

If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], then the value of (p+q) is_______>

If range of function f(x)=sin^(-1)x+2tan^(-1)x+x^2+4x+1 is [p , q], then the value of (p+q) is_______>

The vertices of triangle are A(-5,3),B(p-1) and C(6,q). If the centroid of the DeltaABC is (1,-1) , then the values of p and q are (i) p=-2,q=5 (ii) p=2,q=-5 (iii) p=3,q=5 (iv) p=-5,q=2

Find the values of p\ a n d\ q so that x^4+p x^3+2x^2-3x+q is divisible by (x^2-1)

In the quadratic equation x^2+(p+i q)x+3i=0,p&q are real. If the sum of the squares of the roots is 8 then: p=3,q=-1 b. p=3,q=1 c. p=-3,q=-1 d. p=-3,q=1