Advertisements
Advertisements
प्रश्न
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
Advertisements
उत्तर
Given that,
x = `"t" + 1/"t"`, y = `"t" - 1/"t"`
Differentiating both the given parametric functions w.r.t. t
`"dx"/"dt" = 1 - 1/"t"^2`, `"dy"/"dt" = 1 + 1/"t"^2`
∴ `"dy"/"dx" = (("dy")/("dt"))/(("dx")/("dt"))`
= `(1 + 1/"t"^2)/(1 - 1/"t"^2)`
= `("t"^2 + 1)/("t"^2 - 1)`
Hence, `"dy"/"dx" = ("t"^2 + 1)/("t"^2 - 1)`.
APPEARS IN
संबंधित प्रश्न
find dy/dx if x=e2t , y=`e^sqrtt`
If x=at2, y= 2at , then find dy/dx.
If `x=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`
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 = cos t (3 – 2 cos2 t) and y = sin t (3 – 2 sin2 t), find the value of dx/dy at t =4/π.
If x and y are connected parametrically by the equations, without eliminating the parameter, find `bb(dy/dx)`.
x = 2at2, y = at4
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 = 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`.
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 X = f(t) and Y = g(t) Are Differentiable Functions of t , then prove that y is a differentiable function of x and
`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`
Hence find `"dy"/"dx"` if x = a cos2 t and y = a sin2 t.
IF `y = e^(sin-1x) and z =e^(-cos-1x),` prove that `dy/dz = e^x//2`
If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
Evaluate : `int (sec^2 x)/(tan^2 x + 4)` dx
x = `"e"^theta (theta + 1/theta)`, y= `"e"^-theta (theta - 1/theta)`
sin x = `(2"t")/(1 + "t"^2)`, tan y = `(2"t")/(1 - "t"^2)`
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 = 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 ____________.
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
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 ______.
