Podcast
Questions and Answers
If the parametric equation of a curve is given by x = et cos t, y = et sin t, then the tangent to the curve at the point makes with the x-axis an angle of
If the parametric equation of a curve is given by x = et cos t, y = et sin t, then the tangent to the curve at the point makes with the x-axis an angle of
For the parabola y² = 4ax, the ratio of the subtangent to the abscissa is
For the parabola y² = 4ax, the ratio of the subtangent to the abscissa is
If y = 4x - 5 is a tangent to the curve y² = px³ + q at (2,3), then
If y = 4x - 5 is a tangent to the curve y² = px³ + q at (2,3), then
The length of the normal to the curve y = a²(et/x + e-x/a) is
The length of the normal to the curve y = a²(et/x + e-x/a) is
Signup and view all the answers
If the area of the triangle enclosed between the axes and any tangent to the curve xy = aⁿ is constant, then n is
If the area of the triangle enclosed between the axes and any tangent to the curve xy = aⁿ is constant, then n is
Signup and view all the answers
The tangent lines drawn from the origin to the curve y = cos x have their points of contact lying on the curve
The tangent lines drawn from the origin to the curve y = cos x have their points of contact lying on the curve
Signup and view all the answers
What is the value of the expression ∫(f'(x) f''(x) / f'(x)) dx from 0 to π/4?
What is the value of the expression ∫(f'(x) f''(x) / f'(x)) dx from 0 to π/4?
Signup and view all the answers
What are the coordinates of the point R on the parabola y^2 = 2x, where the tangent to the curve is parallel to the chord PQ?
What are the coordinates of the point R on the parabola y^2 = 2x, where the tangent to the curve is parallel to the chord PQ?
Signup and view all the answers
What is the equation of the normal to the curve y^2 = x^3 at the point whose abscissa is 8?
What is the equation of the normal to the curve y^2 = x^3 at the point whose abscissa is 8?
Signup and view all the answers
What is the number of tangents to the curve x^(3/2) + y^(3/2) = a^(3/2) that are equally inclined to the axes?
What is the number of tangents to the curve x^(3/2) + y^(3/2) = a^(3/2) that are equally inclined to the axes?
Signup and view all the answers
What are the coordinates of the points on the curve 9y^2 = x^3 where the normal to the curve cuts equal intercepts from the axes?
What are the coordinates of the points on the curve 9y^2 = x^3 where the normal to the curve cuts equal intercepts from the axes?
Signup and view all the answers
What is the change of the slope of the tangent to the curve at θ = 89.60 degrees?
What is the change of the slope of the tangent to the curve at θ = 89.60 degrees?
Signup and view all the answers
What is the condition for the curves $y^2 = 2x^3$ and $4x - 3y + 2 = 0 to be perpendicular to each other at a point?
What is the condition for the curves $y^2 = 2x^3$ and $4x - 3y + 2 = 0 to be perpendicular to each other at a point?
Signup and view all the answers
What is the equation of the normal to the parabola $y^2 = 4ax$ at a point $P$?
What is the equation of the normal to the parabola $y^2 = 4ax$ at a point $P$?
Signup and view all the answers
What is the length of the normal at any point on the catenary curve $y = c \/cosh\left(\frac{x}{c}\right)$?
What is the length of the normal at any point on the catenary curve $y = c \/cosh\left(\frac{x}{c}\right)$?
Signup and view all the answers
What is the value of tanθ at the point P(2, 3) on the given curves?
What is the value of tanθ at the point P(2, 3) on the given curves?
Signup and view all the answers
What is the length of the tangent PA at point P(x, y) on the curve y = f(x)?
What is the length of the tangent PA at point P(x, y) on the curve y = f(x)?
Signup and view all the answers
What is the condition for the tangent and normal to intersect at right angles at a point P on the curve?
What is the condition for the tangent and normal to intersect at right angles at a point P on the curve?
Signup and view all the answers
What is the meaning of the subtangent and subnormal at a point P on the curve y = f(x)?
What is the meaning of the subtangent and subnormal at a point P on the curve y = f(x)?
Signup and view all the answers
What is the significance of the point P in the context of tangents and normals?
What is the significance of the point P in the context of tangents and normals?
Signup and view all the answers
If the area of the triangle enclosed between the axes and any tangent to the curve xy = aⁿ is constant, then n is
If the area of the triangle enclosed between the axes and any tangent to the curve xy = aⁿ is constant, then n is
Signup and view all the answers
The tangent to the curve y² = px³ + q at (2, 3) is y = 4x - 5. Then, what are the values of p and q?
The tangent to the curve y² = px³ + q at (2, 3) is y = 4x - 5. Then, what are the values of p and q?
Signup and view all the answers
The length of the normal to the curve y = a²(et/x + e-x/a) is
The length of the normal to the curve y = a²(et/x + e-x/a) is
Signup and view all the answers
What is the equation of the curve on which the tangents drawn from the origin to the curve y = cos x have their points of contact?
What is the equation of the curve on which the tangents drawn from the origin to the curve y = cos x have their points of contact?
Signup and view all the answers
For the parabola y² = 4ax, the ratio of the subtangent to the abscissa is
For the parabola y² = 4ax, the ratio of the subtangent to the abscissa is
Signup and view all the answers
If at each point of the curve y = x³ - ax² + x + 1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then
If at each point of the curve y = x³ - ax² + x + 1, the tangent is inclined at an acute angle with the positive direction of the x-axis, then
Signup and view all the answers
What is the geometrical significance of the derivative of a function at a point?
What is the geometrical significance of the derivative of a function at a point?
Signup and view all the answers
If the function y = f(x) is increasing in an interval, then its derivative f'(x) in that interval is
If the function y = f(x) is increasing in an interval, then its derivative f'(x) in that interval is
Signup and view all the answers
The maximum or minimum value of a function occurs at a point where the
The maximum or minimum value of a function occurs at a point where the
Signup and view all the answers
What is the rate of change of the function y = x³ - 3x² + 2x + 1 at x = 1?
What is the rate of change of the function y = x³ - 3x² + 2x + 1 at x = 1?
Signup and view all the answers
