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Evaluate the following:
`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`
Concept: undefined >> undefined
Evaluate the following:
`int "dt"/sqrt(3"t" - 2"t"^2)`
Concept: undefined >> undefined
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If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:
Concept: undefined >> undefined
Derivative of cot x° with respect to x is ____________.
Concept: undefined >> undefined
Find: `int (dx)/sqrt(3 - 2x - x^2)`
Concept: undefined >> undefined
Show that the lines: `(1 - x)/2 = (y - 3)/4 = z/(-1)` and `(x - 4)/3 = (2y - 2)/(-4) = z - 1` are coplanar.
Concept: undefined >> undefined
If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.
Concept: undefined >> undefined
The position vectors of three consecutive vertices of a parallelogram ABCD are `A(4hati + 2hatj - 6hatk), B(5hati - 3hatj + hatk)`, and `C(12hati + 4hatj + 5hatk)`. The position vector of D is given by ______.
Concept: undefined >> undefined
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
Concept: undefined >> undefined
If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.
Concept: undefined >> undefined
Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.
Concept: undefined >> undefined
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Concept: undefined >> undefined
Read the following passage and answer the questions given below:
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The relation between the height of the plant ('y' in cm) with respect to its exposure to the sunlight is governed by the following equation y = `4x - 1/2 x^2`, where 'x' is the number of days exposed to the sunlight, for x ≤ 3.
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- Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
- Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?
Concept: undefined >> undefined
Find the distance between the point (7, 2, 4) and the plane determined by the points A(2, 5, −3), B(−2, −3, 5) and C(5, 3, −3).
Concept: undefined >> undefined
Differentiate xsinx+(sinx)cosx with respect to x.
Concept: undefined >> undefined
Evaluate `int_(-2)^2x^2/(1+5^x)dx`
Concept: undefined >> undefined
Find the distance of a point (2, 5, −3) from the plane `vec r.(6hati-3hatj+2 hatk)=4`
Concept: undefined >> undefined
Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x − y + z = 0. Also find the distance of the plane, obtained above, from the origin.
Concept: undefined >> undefined
In the given cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(0, 0, 0) 3x – 4y + 12 z = 3
Concept: undefined >> undefined
In the given cases, find the distance of each of the given points from the corresponding given plane
Point Plane
(3, – 2, 1) 2x – y + 2z + 3 = 0
Concept: undefined >> undefined
