Advertisements
Advertisements
प्रश्न
Find the slope of the tangent to the curve y = x3 − 3x + 2 at the point whose x-coordinate is 3.
Advertisements
उत्तर
APPEARS IN
संबंधित प्रश्न
Find the equations of the tangent and normal to the curve x = a sin3θ and y = a cos3θ at θ=π/4.
Find the equation of tangents to the curve y= x3 + 2x – 4, which are perpendicular to line x + 14y + 3 = 0.
Find points at which the tangent to the curve y = x3 − 3x2 − 9x + 7 is parallel to the x-axis.
Find a point on the curve y = (x − 2)2 at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x2 at (0, 0)
Show that the normal at any point θ to the curve x = a cosθ + a θ sinθ, y = a sinθ – aθ cosθ is at a constant distance from the origin.
Find the slope of the tangent and the normal to the following curve at the indicted point x = a (θ − sin θ), y = a(1 − cos θ) at θ = π/2 ?
Find the point on the curve y = 3x2 + 4 at which the tangent is perpendicular to the line whose slop is \[- \frac{1}{6}\] ?
Find the points on the curve \[\frac{x^2}{9} + \frac{y^2}{16} = 1\] at which the tangent is parallel to y-axis ?
Find the points on the curve y = x3 where the slope of the tangent is equal to the x-coordinate of the point ?
Find the equation of the tangent and the normal to the following curve at the indicated point xy = c2 at \[\left( ct, \frac{c}{t} \right)\] ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4x at (1, 2) ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4ax at (x1, y1)?
Find the equation of the tangent and the normal to the following curve at the indicated points:
x = 3cosθ − cos3θ, y = 3sinθ − sin3θ?
Find the equation of the tangent to the curve \[y = \sqrt{3x - 2}\] which is parallel to the 4x − 2y + 5 = 0 ?
Find the angle of intersection of the following curve x2 = 27y and y2 = 8x ?
Show that the following set of curve intersect orthogonally x2 + 4y2 = 8 and x2 − 2y2 = 4 ?
Show that the following curve intersect orthogonally at the indicated point x2 = y and x3 + 6y = 7 at (1, 1) ?
Show that the curves 4x = y2 and 4xy = k cut at right angles, if k2 = 512 ?
Prove that the curves y2 = 4x and x2 + y2 - 6x + 1 = 0 touch each other at the point (1, 2) ?
Find the slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to x-axis, then write the value of \[\frac{dy}{dx}\] ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of \[\frac{dx}{dy}\] ?
The equation of the normal to the curve y = x + sin x cos x at x = `π/2` is ___________ .
If the tangent to the curve x = a t2, y = 2 at is perpendicular to x-axis, then its point of contact is _____________ .
The slope of the tangent to the curve x = t2 + 3 t − 8, y = 2t2 − 2t − 5 at point (2, −1) is ________________ .
The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 is ______________ .
The equation of the normal to the curve x = a cos3 θ, y = a sin3 θ at the point θ = π/4 is __________ .
The point on the curve 9y2 = x3, where the normal to the curve makes equal intercepts with the axes is
(a) \[\left( 4, \frac{8}{3} \right)\]
(b) \[\left( - 4, \frac{8}{3} \right)\]
(c) \[\left( 4, - \frac{8}{3} \right)\]
(d) none of these
Find the equation of tangent to the curve y = x2 +4x + 1 at (-1 , -2).
Find the equation of all the tangents to the curve y = cos(x + y), –2π ≤ x ≤ 2π, that are parallel to the line x + 2y = 0.
The equation of the normal to the curve y = sinx at (0, 0) is ______.
At what points on the curve x2 + y2 – 2x – 4y + 1 = 0, the tangents are parallel to the y-axis?
The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is ______.
For which value of m is the line y = mx + 1 a tangent to the curve y2 = 4x?
The slope of the tangent to the curve x = a sin t, y = a{cot t + log(tan `"t"/2`)} at the point ‘t’ is ____________.
Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A and B, respectively. If C is the centre of the circle through the points P, A and B and ∠CPB = θ, then a value of tan θ is:
If the tangent to the curve y = x + siny at a point (a, b) is parallel to the line joining `(0, 3/2)` and `(1/2, 2)`, then ______.
If the tangent to the conic, y – 6 = x2 at (2, 10) touches the circle, x2 + y2 + 8x – 2y = k (for some fixed k) at a point (α, β); then (α, β) is ______.
