Search & Filtering
i. about the x-axis
ii. about the y-axis.
Give each answer as a multiple of π.
Q. Show that P and Q lie on opposite side of the x-axis and calculate the finite
area bounded by the chord and the arc PQ of the parabola.
tangent to the curve at O, the origin, intersects the curve again at P. Calculate
i. the finite area bounded by the curve and OA,
ii. the finite area bounded by the curve and OP
(1) It is assumed that the volume of every particle is 6.4π x 10^-12 cm^3.
(2) The height of the vase is 32 cm; and
(3) The equation of the curve that the vase made of is given by y=x^2 - 6 wit domain x≥ -2.
To win this game, calculate the exact number of particles that can be placed in the vase.
A piece of wire 20 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is: (a) maximum? (b) minimum?
find workdone integral of F.dr where f(x,y,z)=e^2*x+z(y+1)j+z^3k along the curve C r(t)=t^3i+(1-3t)j+e^tk for 0<=t<=2
e {𝑎𝑛 }𝑛=1 ∞ is defined by 𝑎𝑛 = 2𝑛−3 3𝑛+4 for 𝑛 ∈ ℕ Prove that {𝑎𝑛 }𝑛=1 ∞ is a bounded sequence. iii) Find lim𝑛→∞ 𝑎�
Let 𝑓(𝑡) = 𝑒 −(𝑡−1) 2 describes the position of a particle at time 𝑡 ≥ 0. a) What is the initial displacement? b) Find the critical points of 𝑓(𝑡). c) Find the intervals of positive and negative velocities of the particle. d) Find the time where particle changes from acceleration to deceleration and vice versa. e) Find the maximum displacement of the particle. f) Sketch the graph of 𝑓(𝑡). [
𝑓(𝑥) = 𝑒 −𝑥 1+𝑒−𝑥 . i) Determine whether 𝑓(𝑥) is a one-to-one function.
