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प्रश्न
Find the slope of the tangent to curve y = x3 − x + 1 at the point whose x-coordinate is 2.
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उत्तर
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संबंधित प्रश्न
Find the equation of the normal at a point on the curve x2 = 4y which passes through the point (1, 2). Also find the equation of the corresponding tangent.
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(A) 3
(B) 1/3
(C) −3
(D) `-1/3`
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Find the equation of the normal to y = 2x3 − x2 + 3 at (1, 4) ?
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Find the equation of the tangent and the normal to the following curve at the indicated points x = asect, y = btant at t ?
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Find the equation of the tangent to the curve \[y = \sqrt{3x - 2}\] which is parallel to the 4x − 2y + 5 = 0 ?
Show that the following set of curve intersect orthogonally x3 − 3xy2 = −2 and 3x2y − y3 = 2 ?
Show that the curves 4x = y2 and 4xy = k cut at right angles, if k2 = 512 ?
Find the slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?
Write the angle between the curves y2 = 4x and x2 = 2y − 3 at the point (1, 2) ?
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The point on the curve y = x2 − 3x + 2 where tangent is perpendicular to y = x is ________________ .
The equation of the normal to the curve 3x2 − y2 = 8 which is parallel to x + 3y = 8 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 y = 2 sin2 x and y = cos 2 x at \[x = \frac{\pi}{6}\] is ____________ .
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(a) \[\left( 4, \frac{8}{3} \right)\]
(b) \[\left( - 4, \frac{8}{3} \right)\]
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(d) none of these
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Prove that the curves xy = 4 and x2 + y2 = 8 touch each other.
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Find the equation of the normal lines to the curve 3x2 – y2 = 8 which are parallel to the line x + 3y = 4.
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Find the equation to the tangent at (0, 0) on the curve y = 4x2 – 2x3
