Home
Class 12
MATHS
Find equation of tangent to y =e^(x) at ...

Find equation of tangent to y `=e^(x)` at x=0 . Hence draw graph

Text Solution

Verified by Experts

`At x=0 " "rArr " "y=e^(0) =1`
`(dy)/(dx) " "=" "e^(x) " "rArr " "(dy)/(dx)|_(x=0)=1`

Hence equation of tangent is
` 1(x -0) =(y -1)`
`rArr" "y=x+1`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Self Practice Problems|36 Videos
  • APPLICATION OF DERIVATIVES

    RESONANCE ENGLISH|Exercise Exersise -1A|5 Videos
  • COMBINATORICS

    RESONANCE ENGLISH|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|5 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the tangent to x^(2) + y^(2) - 2x + 4y=0 " at" (3,-1) Also find the equation of tangent parallel to it.

The equation of the tangent to the curve y = e^(2x) at (0,1) is

Find the equation of the tangent of the parabola y^(2) = 8x which is perpendicular to the line 2x+ y+1 = 0

Find the equation of tangents to hyperbola x^(2)-y^(2)-4x-2y=0 having slope 2.

Find the equation of tangent to the hyperbola y=(x+9)/(x+5) which passes through (0, 0) origin

To find the point of contact P (x_1, y_1) of a tangent to the graph of y = f(x) passing through origin O , we equate the slope of tangent to y = f(x) at P to the slope of OP . Hence we solve the equation f' (x) = f(x_1)/x_1 to get x_1 and y_1 .Now answer the following questions (7 -9): The equation |lnmx|= px where m is a positive constant has a single root for

Find the equation of tangent of tangent of the curve y = b * e^(-x//a) at that point at which the curve meets the Y-axis.

Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1)

Find the equation of tangent to the conic x^2-y^2-8x+2y+11=0 at (2,1) .

Find the equation of the tangent to the circle x^2+y^2-2x-2y-23=0 and parallel to 2x+y+3=0.

RESONANCE ENGLISH-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. Find equation of tangent to y =e^(x) at x=0 . Hence draw graph

    Text Solution

    |

  2. A particle moving on a curve has the position at time t given by x=f'(...

    Text Solution

    |

  3. Find the interval in which f(x) = xsqrt(4ax-x^2), (alt0) is decreasing

    Text Solution

    |

  4. If the function f:[0,4]vecR is differentiable, the show that for a , b...

    Text Solution

    |

  5. if all the function f(x)=a^2x^3-a/9x^2-2x-b arepositive and the minimu...

    Text Solution

    |

  6. if f(x) = {underset(a^(2) -2+ (sin (x-K))/(x-K))(3+|x-k|)," "underse...

    Text Solution

    |

  7. The equation x^3-3x+[a]=0, where [*] denotes the greatest integer func...

    Text Solution

    |

  8. Let f(x) =sin ({x})/(a) + cos ({x})/(a) where a gt 0 and {.} denotes t...

    Text Solution

    |

  9. A function f(x) having the following properties, (i) f(x) is conti...

    Text Solution

    |

  10. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

    Text Solution

    |

  11. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,\ -1) , find the val...

    Text Solution

    |

  12. if A be the area of a triangle, prove that the error in A resulting fr...

    Text Solution

    |

  13. Find the possible values of a such that the inequality 3-x^(2)gt|x-a| ...

    Text Solution

    |

  14. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

    Text Solution

    |

  15. Find the interval of increase and decrease for the function g(x) =...

    Text Solution

    |

  16. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  17. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  18. For any acute angled triangleABC,(sinA)/(A)+(sinB)/(B)+(sinC)/(C ) can

    Text Solution

    |

  19. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

    Text Solution

    |

  20. Show that height of the cylinder of greatest volume which can be in...

    Text Solution

    |

  21. The cosine of the angle at the vertex of an isosceles triangle having ...

    Text Solution

    |