Home
Class 12
MATHS
Find ("lim")(xvec0){tan(pi/4+x)}^(1//x)...

Find `("lim")_(xvec0){tan(pi/4+x)}^(1//x)`

Text Solution

Verified by Experts

The correct Answer is:
`e^(2)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL CALCULUS

    VMC MODULES ENGLISH|Exercise JEE main (Archive)|51 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

Evaluate lim_(xto0){tan((pi)/4+x)}^(1/x)

If (lim)_(xvec0)[cot(pi/4+x)]^(1//x)=A e^2 then the value of A is: e^2 (B) e^(-4) (C) e (D) e^3

The value of lim_(xrarr0){tan((pi)/(4)+x)}^(1//x) , is

("lim")_(xvec1)(1-x)tan(pix)/2=_____

Evaluate: ("lim")_(xvec0) ((1+x)^(1/x)-e+1/2e x)/(x^2)

Evaluate the limits using the expansion formula of functions ("lim")_(xvec0)(e^x-1-x)/(x^2)

Evaluate: ("lim")_(xvec0)(tanx-sinx)/(x^3)

Evaluate the limits using the expansion formula of functions ("lim")_(xvec0){(sinx-x+(x^3)/6)/(x^5)}

Evaluate: ("lim")_(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

Evaluate ("lim")_(xvec0)((sinx)/x)^(((sinx)/(x-sinx)))

VMC MODULES ENGLISH-DIFFERENTIAL CALCULUS-JEE Advanced (Archive)
  1. Let g(x) be a polynomial of degree one and f(x) is defined by f(x)={g...

    Text Solution

    |

  2. Let f be a continuous, g be a discontinuous function. Prove that f + g...

    Text Solution

    |

  3. Let f(x) be continuous function satisfying the condition f(-x) = f...

    Text Solution

    |

  4. Let R be the set of real numbers and f : R to R be such that for all x...

    Text Solution

    |

  5. The points where the function f(x) = [x] + |1 - x|, -1 < x < 3 where [...

    Text Solution

    |

  6. The values of a and b so that the function f(x) = {{:(x + a sqrt(2) si...

    Text Solution

    |

  7. If x=s e ctheta-costhetaa n dy=sec^ntheta-cos^ntheta,p rov et h a t ...

    Text Solution

    |

  8. A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y...

    Text Solution

    |

  9. Given that f(x)= {((1-cos4x)/(x^(2))",","if "x lt 0),(a",","if "x =0),...

    Text Solution

    |

  10. Find (dy)/(dx) at x=-1, when (siny)^(sin.(pix)/(2))+(sqrt3)/(2)sec^(-1...

    Text Solution

    |

  11. Find ("lim")(xvec0){tan(pi/4+x)}^(1//x)

    Text Solution

    |

  12. Let f(x) = {{:({1 + |sin x|}^(a//|sin x|)",",-pi//6 lt x lt 0),(b",",x...

    Text Solution

    |

  13. Let f((x+y)/(2))= (f(x)+f(y))/(2) for all real x and y. If f'(0) exits...

    Text Solution

    |

  14. If f(x)={xe^-[1/(|x|)+1/x]; x != 0; 0;x=0 Prove that f(x) is not diff...

    Text Solution

    |

  15. Determine the values of x for which the following functions fails to b...

    Text Solution

    |

  16. "If "=(ax^(2))/((x-a)(x-b)(x-c))+(bx)/((x-b)(x-c))+(c)/(x-c)+1," prove...

    Text Solution

    |

  17. Let alpha in R. Prove that a function f: RtoR is differentiable a...

    Text Solution

    |

  18. Q. f={(x+a if x<0), (|x-1| if x>=0) g(x)={(x+1 if x<0),(x-1)^2 + b ...

    Text Solution

    |

  19. f(x)={bsin^-1((x+c)/2),-1/2 lt xlt0 and 1/2 , x=0 and e^(((ax)/2)-1)/...

    Text Solution

    |

  20. If |cos^-1(1)/(n)|lt (pi)/(2), then lim(n to oo) {(n+1)(2)/(pi)cos^-...

    Text Solution

    |