Home
Class 12
MATHS
f(x)={(x^2+e^(1/(2-x)))^(-1)k ,x=2, x!=2...

`f(x)={(x^2+e^(1/(2-x)))^(-1)k ,x=2, x!=2` is continuous from right at the point `x=2,` then `k` equals
a. `0`
b. `1//4`
c. `-1//4`
d. none of these

A

0

B

1\4

C

`-1//4`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
`k=underset(xrarr2^(+))(lim)(x^(2)+e^((1)/(2-x)))^(-1)`
`therefore" "k=underset(hrarr0)(lim)[(2+h)^(2)+e^((-1)/(4))]^(-1)`
`=(4+e^(-oo))^(-1)`
`=1//4`
Promotional Banner

Topper's Solved these Questions

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|102 Videos

  • COORDINATE SYSTEM

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|2 Videos

Similar Questions

Explore conceptually related problems

f(x)={(x^2+e^(1/(2-x)))^(-1), x!=2 k ,x=2 is continuous from right at the point x=2, then k equals a. 0 b. 1//4 c. -1//4 d. none of these

If f(x)=-1+|x-2|, 0lexle4 g(x)=2-|x|, -1lexle3 Then, fog(x) is continuous for x belonging to

If f(x)={((sin5x)/(x^(2)+2x),"when "x ne 0),(k+(1)/(2),"when "x =0):} is continuous at x=0, then the value of k is-

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

If the function f(x)=((128 a+a x)^(1/8)-2)/((32+b x)^(1/5)-2) is continuous at x=0 , then the value of a/b is (A) 3/5f(0) (B) 2^(8/5)f(0) (C) (64)/5f(0) (D) none of these

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to (a) 0 (b) 2pi (c) pi (d) none of these

The function f(x) is defined by f(x)= {{:((x^(2) +e ^((1)/(2-x)))^(-1)",", "when" x ne2),(k "," ,"when" x =2):} If lim _(xto^(2+)) f(x) =f(2), then k is equal to-

If f(x)={(|x|-3 when x = 1) & g(x)={2-|x| when x = 2 . if h(x)=f(x)+g(x) is discontinuous at exactly one point, then - (a). a=-3, b=0 (b). a=-3, b=-1 (c) a=2, b=1 (d) a=0, b=1

int_(-1)^2[([x])/(1+x^2)]dx ,w h e r e[dot] denotes the greater integer function, is equal to (a) -2 (b) -1 (c) 0 (d) none of these

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

CENGAGE PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-All Questions
  1. If f(x)={sin(pi/2)(x-[x]),x<5 5(b-1),x=5(a b^2|x^2-11 x+24|)/(x-3),x >...

    Text Solution

    |

  2. The function f(x) is discontinuous only at x=0 such that f^2(x)=1AAx i...

    Text Solution

    |

  3. f(x)={(x^2+e^(1/(2-x)))^(-1)k ,x=2, x!=2 is continuous from right at t...

    Text Solution

    |

  4. If the function f(x)=((128 a+a x)^(1//8)-2)/((32+b x)^(1//5)-2) is con...

    Text Solution

    |

  5. If f(x)={(1-cos(1-cos x/2))/(2^m x^n)1x=0,x!=0 is continous at x=0 the...

    Text Solution

    |

  6. f is a continous function in [a, b]; g is a continuous function in [b,...

    Text Solution

    |

  7. If the function f(x) defined as f(x) defined as f(x)={3,x=0(1+(a x+b x...

    Text Solution

    |

  8. Let f(x)={((alpha cotx)/x+beta/x^2 ,, 0<|x|lt=1),(1/3 ,, x=0):}. If f...

    Text Solution

    |

  9. Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly...

    Text Solution

    |

  10. Let f(x)=[t a n x[cot x]],x [pi/(12),pi/(12)] , (where [.] denotes the...

    Text Solution

    |

  11. Number of points of discontinuity of f(x)=[sin^(-1)x]-[x] in its domai...

    Text Solution

    |

  12. If g(x)=(lim)(mvecoo)(x^mf(x)+h(x)+3)/(2x^m+4x+1) when x!=1a n dg(1)=e...

    Text Solution

    |

  13. The number of points of discontinuity of fx)=[2x^2]-{2x2}^2 (where [] ...

    Text Solution

    |

  14. If f(x)={(|x|-3 when x < 1), and (|x-2|+a , when x >= 1) & g(x)={2...

    Text Solution

    |

  15. The function f(x)=(x^3)/8-s inpix+4in[-4,4] does not take the value -4...

    Text Solution

    |

  16. Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-...

    Text Solution

    |

  17. Let f(x)={{:(x[(1)/(x)]+x[x],if, x ne0),(0,if,x=0):} (where [x] denote...

    Text Solution

    |

  18. A function f: RvecR is defined as f(x)=(lim)(nvecoo)(a x^2+b x+c+e^(n ...

    Text Solution

    |

  19. If is an even function such that lim(h rarr 0) (f(h)-f(0))/(h) has som...

    Text Solution

    |

  20. Number of point where function f(x) defined as f:[0,2pi] rarrR,f(x)={{...

    Text Solution

    |