Home
Class 12
MATHS
if f(x) = {{:(x+2",",xle-1),(cx^(2)",",x...

if `f(x) = {{:(x+2",",xle-1),(cx^(2)",",xgt-1):},` then find c when `lim(xto-1)f(x)` exists.

Text Solution

Verified by Experts

The correct Answer is:
-1
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL -1|134 Videos
  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise LEVEL 2|103 Videos
  • CONIC SECTIONS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|76 Videos
  • DIFFERENTIAL CALCULUS 2

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|81 Videos

Similar Questions

Explore conceptually related problems

Let f(x)={:{(x+2",",xle-1),(cx^(2)",",xgt-1):} If Lt_(xto-1) f(x) exists, then c is (i) -1 (ii) 1 (iii) 2 (iv) -2

If f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)" if exists.

Let f(x)={{:(5x-4",",0ltxle1),(4x^(3)-3x",",1ltxlt2.):} Find lim_(xto1)f(x).

If f(x)={{:(2x-1,"when "xle0),(x^(2),"when "xgt0):},"then find "f((1)/(2)) and f((-1)/(2))

If f(x)={{:(sinx","" "xnenpi", "ninI),(2","" ""otherwise"):} and g(x)={{:(x^(2)+1","" "xne0", "2),(4","" "x=0),(5","" "x=2):} then find lim_(xto0) g{f(x)} .

Evaluate the left- and right-hand limits of the function defined f(x)={{:(1+x^(2)",if "0lexlt1),(2-x", if" xgt1):}"at "x=1. "Also, show that lim_(xto1) f(x) does not exist.

If f(x) is defined as f(x)={{:(x,0le,xle1),(1,x,=1),(2-x,x,gt1):} then show that lim_(Xrarr1) f(x)=1

Evaluate the left hand and right hand limits of the function defined by f(x)={(1+x^(2)", if "0lexle1),(2-x^(2)", if "xgt1):}" at "x=1 also, show that lim f(x) does not exist.

If f(x)={{:(x^(2),xle0),(x,xgt0):} and g(x)=-absx,x inR, then find fog .

Let f(x) =e^(x-1)-ax^(2)+b and g(x)={{:(e^(x-1),xle1),(x^(2)+1,xgt1):}, then find the values of a and b such that f(x) xx g(x) is differentiable at x=1 .

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. if f(x) = {{:(x+2",",xle-1),(cx^(2)",",xgt-1):}, then find c when lim(...

    Text Solution

    |

  2. Let g: R -> R be a differentiable function with g(0) = 0,,g'(1)!=0.Let...

    Text Solution

    |

  3. Let f(x)=sin((pi)/(6)sin((pi)/(2)sinx)) " for all "x in R and g(x)=(pi...

    Text Solution

    |

  4. Let f:R to R and h:R to R be differentiable functions such that f(x)=x...

    Text Solution

    |

  5. Let a , b in R and f:R to R be defined by f(x) =a cos (|x^(3)-x|)+...

    Text Solution

    |

  6. Let f:[-1/2,2] rarr R and g:[-1/2,2] rarr R be functions defined by f(...

    Text Solution

    |

  7. Let [x] be the greatest integer less than or equal to x . Then ,...

    Text Solution

    |

  8. Let f(x)=(1-x(1+|1-x|))/(|1-x|)cos((1)/(1-x))" for "x ne1. then

    Text Solution

    |

  9. Let f be two differentiable function satisfying f(1)=1,f(2)=4, f(3)=9,...

    Text Solution

    |

  10. If f''(x) =- f(x) and g(x) = f'(x) and F(x)=(f((x)/(2)))^(2)+(g((x)/(2...

    Text Solution

    |

  11. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)...

    Text Solution

    |

  12. underset(xrarr(pi)/(4))(lim)(int(2)^(sec^(2)x)f(t)dt)/(x^(2-)(pi^(2))/...

    Text Solution

    |

  13. (d^2x)/(dy^2) equals: ((d^2y)/(dx^2))^(-1) (b) -((d^2y)/(dx^2))^(-1)(...

    Text Solution

    |

  14. Let g(x) = log f(x), where f(x) is a twice differentiable positive fun...

    Text Solution

    |

  15. Let g(x)=((x-1)^(n))/(logcos^(m)(x-1)),0ltxlt2 m and n integers, m ne0...

    Text Solution

    |

  16. If underset(xto0)lim[1+xln(1+b^(2))]^(1//x)=2bsin^(2)theta,bgt0," and ...

    Text Solution

    |

  17. Let f(x) = {{:(x^(2)|"cos"(pi)/(x)|",",x ne 0","x in R),(0",",x = 0):}...

    Text Solution

    |

  18. If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

    Text Solution

    |

  19. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

    Text Solution

    |

  20. Check the differentiability if f(x) = min. {1, x^(2), x^(3)}.

    Text Solution

    |

  21. Let f(x) be a non-constant twice differentiable function defined on (-...

    Text Solution

    |