Advertisements
Advertisements
प्रश्न
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at ______.
विकल्प
(0, 1)
`(- 1/2, 0)`
(2, 0)
(0, 2)
Advertisements
उत्तर
The tangent to the curve y = e2x at the point (0, 1) meets x-axis at `(- 1/2, 0)`.
Explanation:
Equation of the curve is y = e2x
Slope of the tangent `"dy"/"dx"` = 2e2x
⇒ `"dy"/"dx"_(0, 1)` = 2 · e0 = 2
∴ Equation of tangent to the curve at (0, 1) is
y –1 = 2(x – 0)
⇒ y – 1 = 2x
⇒ y – 2x = 1
Since the tangent meets x-axis where y = 0
∴ 0 – 2x = 1
⇒ x = `(-1)/2`
So the point is `(- 1/2, 0)`.
APPEARS IN
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.
Find the point on the curve y = x3 − 11x + 5 at which the tangent is y = x − 11.
Find the equations of the tangent and normal to the given curves at the indicated points:
y = x3 at (1, 1)
Show that the tangents to the curve y = 7x3 + 11 at the points where x = 2 and x = −2 are parallel.
For the curve y = 4x3 − 2x5, find all the points at which the tangents passes through the origin.
Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1. [Hint: Two curves intersect at right angle if the tangents to the curves at the point of intersection are perpendicular to each other.]
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 points on the curve y = x3 − 2x2 − 2x at which the tangent lines are parallel to the line y = 2x− 3 ?
Find the points on the curve 2a2y = x3 − 3ax2 where the tangent is parallel to x-axis ?
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 equation of the tangent and the normal to the following curve at the indicated point y = x4 − bx3 + 13x2 − 10x + 5 at (0, 5) ?
Find the equation of the tangent and the normal to the following curve at the indicated point y = x4 − 6x3 + 13x2 − 10x + 5 at x = 1?
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 \[x^\frac{2}{3} + y^\frac{2}{3}\] = 2 at (1, 1) ?
Find the equation of the tangent and the normal to the following curve at the indicated point y2 = 4ax at (x1, y1)?
At what points will be tangents to the curve y = 2x3 − 15x2 + 36x − 21 be parallel to x-axis ? Also, find the equations of the tangents to the curve at these points ?
Find the angle of intersection of the following curve \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and x2 + y2 = ab ?
Show that the following curve intersect orthogonally at the indicated point y2 = 8x and 2x2 + y2 = 10 at \[\left( 1, 2\sqrt{2} \right)\] ?
Find the slope of the tangent to the curve x = t2 + 3t − 8, y = 2t2 − 2t − 5 at t = 2 ?
Write the value of \[\frac{dy}{dx}\] , if the normal to the curve y = f(x) at (x, y) is parallel to y-axis ?
If the tangent line at a point (x, y) on the curve y = f(x) is parallel to y-axis, find the value of \[\frac{dx}{dy}\] ?
Write the angle between the curves y = e−x and y = ex at their point of intersections ?
The point on the curve y2 = x where tangent makes 45° angle with x-axis is ______________ .
The point at the curve y = 12x − x2 where the slope of the tangent is zero will be _____________ .
The angle between the curves y2 = x and x2 = y at (1, 1) is ______________ .
The equation of the normal to the curve 3x2 − y2 = 8 which is parallel to x + 3y = 8 is ____________ .
The angle of intersection of the curves xy = a2 and x2 − y2 = 2a2 is ______________ .
Find the equation of tangents to the curve y = cos(x + y), –2π ≤ x ≤ 2π that are parallel to the line x + 2y = 0.
Find the equation of the tangent line to the curve `"y" = sqrt(5"x" -3) -5`, which is parallel to the line `4"x" - 2"y" + 5 = 0`.
The point on the curve y2 = x, where the tangent makes an angle of `pi/4` with x-axis is ______.
Find an angle θ, 0 < θ < `pi/2`, which increases twice as fast as its sine.
Prove that the curves y2 = 4x and x2 + y2 – 6x + 1 = 0 touch each other at the point (1, 2)
The equation of tangent to the curve y(1 + x2) = 2 – x, where it crosses x-axis is ______.
`"sin"^"p" theta "cos"^"q" theta` attains a maximum, when `theta` = ____________.
The tangent to the parabola x2 = 2y at the point (1, `1/2`) makes with the x-axis an angle of ____________.
Let `y = f(x)` be the equation of the curve, then equation of normal is
Find the points on the curve `y = x^3` at which the slope of the tangent is equal to the y-coordinate of the point
The slope of the tangentto the curve `x= t^2 + 3t - 8, y = 2t^2 - 2t - 5` at the point `(2, -1)` is
