Advertisements
Advertisements
प्रश्न
If x = a (2θ – sin 2θ) and y = a (1 – cos 2θ), find `dy/dx` when `theta = pi/3`
Advertisements
उत्तर
Applying parametric differentiation
`dx/(d theta) = 2a - 2acos2theta`
`dy/(d theta) = 0 + 2asin 2theta`
`dy/dx = dy/(d theta) xx (d theta)/dx = (sin 2 theta)/(1-cos 2 theta)`
Now putting the value of `theta = pi/3`
`dy/dx|_(theta = pi/3) = (sin 2(pi/3))/(1-cos2(pi/3))`
`= (sqrt3/2)/(1+ 1/2)`
`= (sqrt3/2)/(3/2) = 1/sqrt3`
So `dy/dx is 1/sqrt3` at `theta = pi/3`
APPEARS IN
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=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`
If y =1 − cos θ, x = 1 − sin θ, then `dy/dx "at" θ =pi/4` is ______
If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`
If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of `dy/dx `at t = `pi/4`
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 and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = a cos θ, y = b cos θ
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 = cos θ – cos 2θ, y = sin θ – sin 2θ
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 sec θ, y = b tan θ
If x = `sqrt(a^(sin^(-1)t))`, y = `sqrt(a^(cos^(-1)t))` show that `dy/dx = - y/x`.
The cost C of producing x articles is given as C = x3-16x2 + 47x. For what values of x, with the average cost is decreasing'?
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
x = 3cosθ – 2cos3θ, y = 3sinθ – 2sin3θ
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`
Differentiate `x/sinx` w.r.t. sin x
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 = t2, y = t3, then `("d"^2"y")/("dx"^2)` is ______.
If y `= "Ae"^(5"x") + "Be"^(-5"x") "x" "then" ("d"^2 "y")/"dx"^2` is equal to ____________.
Form the point of intersection (P) of lines given by x2 – y2 – 2x + 2y = 0, points A, B, C, Dare taken on the lines at a distance of `2sqrt(2)` units to form a quadrilateral whose area is A1 and the area of the quadrilateral formed by joining the circumcentres of ΔPAB, ΔPBC, ΔPCD, ΔPDA is A2, then `A_1/A_2` equals
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 ______.
