Home
Class 12
MATHS
A curve parametrically given by x=t+t^(3...

A curve parametrically given by `x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2)`?

A

`1//3`

B

2

C

3

D

1

Text Solution

Verified by Experts

`(dy)/(dx)=(dy//dt)/(dx//dt)=(2t)/(1+3t^(2))=(1)/(2)`(given)
`rArr" "3t^(2)-4t+1=0`
`rArr" "(3t-1)(t-1)=0`
`rArr" "t=(t)/(3),t=t`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Comprehension)|23 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Matrix)|5 Videos

  • DIFFERENTIATION

    CENGAGE|Exercise Exercise (Single)|137 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE|Exercise Question Bank|25 Videos

  • DOT PRODUCT

    CENGAGE|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

A curve in the xy-plane is parametrically given by x=t+t^(3) and y=t^(2), where t in R is the parameter.For what value (s) of t is (dy)/(dx)=(1)/(2)?(1)/(3) b.2 c.3 d.1

If x=t+(1)/(t) and y=t-(1)/(t) , where t is a parameter,then a value of (dy)/(dx)

The curve described parametrically by x=t^(2)+t+1,y=t^(2)-t+1 represents :

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))

If a curve is represented parametrically by the equation x=f(t) and y=g(t)" then prove that "(d^(2)y)/(dx^(2))=-[(g'(t))/(f'(t))]^(3)((d^(2)x)/(dy^(2)))

Consider the curve represented parametrically by the equation x=t^(3)-4t^(2)-3t and y=2t^(2)+3t-5 where t in R. If H denotes the number of point on the curve where the tangent is horizontal and V the number of point where the tangent is vertical then

A function is reprersented parametrically by the equations x=(1+t)/(t^(3));y=(3)/(2t^(2))+(2)/(t). Then the value of |(dy)/(dx)-x((dy)/(dx))

CENGAGE-DIFFERENTIATION-Exercise (Multiple)
  1. "If "f(theta)=tan (sin^(-1)sqrt((2)/(3+cos 2theta)))," then "

    Text Solution

    |

  2. f(x)=|x^(2)-3x|x|+2|. Then which of the following is/are true ?

    Text Solution

    |

  3. Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1).x then

    Text Solution

    |

  4. If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)...

    Text Solution

    |

  5. If y=x^((logx)^log(logx)) then (dy)/(dx)=

    Text Solution

    |

  6. If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne...

    Text Solution

    |

  7. If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (-2)/(1+x^2) for all ...

    Text Solution

    |

  8. f(n)(x)=e^(f(n-1)(x))" for all "n in N and f(0)(x)=x," then "(d)/(dx){...

    Text Solution

    |

  9. Suppose f and g are functions having second derivatives f' and g' ever...

    Text Solution

    |

  10. If y=e^(-x) cos x and yn+kny=0 where yn=(d^ny)/(dx^n) and kn are const...

    Text Solution

    |

  11. If a function is represented parametrically be the equations x=(1+(lo...

    Text Solution

    |

  12. If y=(x^2)/2+1/2xsqrt(x^2+1)+(log)esqrt(x+sqrt(x^2+1)) , prove that 2y...

    Text Solution

    |

  13. A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in ...

    Text Solution

    |

  14. "If "e^(sin(x^(2)+y^(3)))=tan""(y^(2))/(4)+sin^(-1)x," then y'(0) can ...

    Text Solution

    |

  15. If y=e^(sqrt(x))+e^(-sqrt(x))," then "(dy)/(dx) is equal to

    Text Solution

    |

  16. Let y=sqrt(x+sqrt(x+sqrt(x+...oo)))," then "(dy)/(dx) is equal to

    Text Solution

    |

  17. If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne...

    Text Solution

    |

  18. If a function is represented parametrically be the equations x=(1+(lo...

    Text Solution

    |

  19. "If "y=(x^(2))/(2)+(1)/(2)xsqrt(x^(2)+1)+log(e)sqrt(x+sqrt(x^(2)+1)), ...

    Text Solution

    |

  20. A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in ...

    Text Solution

    |