हिंदी

If x and y are connected parametrically by the equations, without eliminating the parameter, find dy/dx. x = a cos θ, y = b cos θ

Advertisements
Advertisements

प्रश्न

If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a cos θ, y = b cos θ

योग
Advertisements

उत्तर

Given,  x = a cos θ and y = b cos θ

Differentiating both sides with respect to θ,

`dx/(dθ)` = −a sin θ

`dy/(dθ)` = −b sin θ

`dy/dx = (dy/(dθ))/(dx/(dθ))`

= `(-b sin θ)/(- a sin θ)`

= `b/a`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 5: Continuity and Differentiability - Exercise 5.6 [पृष्ठ १८१]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 5 Continuity and Differentiability
Exercise 5.6 | Q 5.6 | पृष्ठ १८१

संबंधित प्रश्न

find dy/dx if x=e2t , y=`e^sqrtt`


If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and  hence, find dy/dx if x=a cost, y=a sint


If x=at2, y= 2at , then find dy/dx.


If y =1 − cos θ, x = 1 − sin θ, then `dy/dx  "at"  θ =pi/4` is ______


 

 If x=a sin 2t(1+cos 2t) and y=b cos 2t(1cos 2t), find `dy/dx `

 

If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1cos 2t), show that `dy/dx=β/αtan t`


If x = a sin 2t (1 + cos 2t) and y = b cos 2t (1 – cos 2t) then find `dy/dx `

 


Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`


If x = cos t (3 – 2 cos2 t) and y = sin t (3 – 2 sin2 t), find the value of dx/dy at t =4/π.


Derivatives of  tan3θ with respect to sec3θ at θ=π/3 is

(A)` 3/2`

(B) `sqrt3/2`

(C) `1/2`

(D) `-sqrt3/2`


If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = sin t, y = cos 2t


If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = a (θ – sin θ), y = a (1 + cos θ)


If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

`x = (sin^3t)/sqrt(cos 2t), y = (cos^3t)/sqrt(cos 2t)`


If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.

x = `a(cos t + log tan  t/2)`, y = a sin t


If x = `sqrt(a^(sin^(-1)t))`, y = `sqrt(a^(cos^(-1)t))` show that `dy/dx = - y/x`.


If `x = acos^3t`, `y = asin^3 t`,

Show that `(dy)/(dx) =- (y/x)^(1/3)`


If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`


If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`


x = `"t" + 1/"t"`, y = `"t" - 1/"t"`


x = 3cosθ – 2cos3θ, y = 3sinθ – 2sin3θ


x = `(1 + log "t")/"t"^2`, y = `(3 + 2 log "t")/"t"`


If x = ecos2t and y = esin2t, prove that `"dy"/"dx" = (-y log x)/(xlogy)`


If x = asin2t (1 + cos2t) and y = b cos2t (1–cos2t), show that `("dy"/"dx")_("at  t" = pi/4) = "b"/"a"`


If x = 3sint – sin 3t, y = 3cost – cos 3t, find `"dy"/"dx"` at t = `pi/3`


If x = sint and y = sin pt, prove that `(1 - x^2) ("d"^2"y")/("dx"^2) - x "dy"/"dx" + "p"^2y` = 0


If `"x = a sin"  theta  "and  y = b cos"  theta, "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.


If y `= "Ae"^(5"x") + "Be"^(-5"x") "x"  "then"  ("d"^2 "y")/"dx"^2` is equal to ____________.


If x = `a[cosθ + logtan  θ/2]`, y = asinθ then `(dy)/(dx)` = ______.


Let a function y = f(x) is defined by x = eθsinθ and y = θesinθ, where θ is a real parameter, then value of `lim_(θ→0)`f'(x) is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×