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Can you make use of the normal curve to find for the probability of a large value? How?
The base of the rectangle is changing at the rate of 3in/min. if its height remains constant, determine the rate of change of its perimeter with respect to time?
Suppose π is odd and differentiable everywhere. Prove that for every positive
number π, there exists a number π in (βπ, π) such that πβ²(π) = π(π)/π.
The Altitude of a triangle is increasing at a rate of 8cm/s while its area is increasing at the rate of 12cm^2/s. At what rate is the base of the triangle changing when the altitude is 20 cm and the area is 100 cm^2 ?
A cone of radius π centimeters and height β centimeters is lowered point first at
a rate of 1 cm/s into a tall cylinder of radius π centimeters that is partially filled with
water. How fast is the water level rising at the instant the cone is completely
submerged
If π(π₯) is a differentiable and π(π₯) = π₯ π(π₯) use the definition of the derivative to show
that πβ²(π₯) = π₯π'(π₯) + π(π₯).
Evaluate the following limits, if they exist, where βπ₯β is the greatest integer function.
(a)lim β2π₯β/π₯
π₯β0
(b) lim π₯ β1/π₯β
π₯β0
How may revolutions per minute must the body make about vertical axis so that the cord make an angle of 45 with the vertical
Let π(π₯) = βπ₯β + ββπ₯β, where βπ₯β is the greatest integer less than or equal to π₯.
(π) For what values of π, does limπ₯βπ
π(π₯)exist?
(π) At what numbers is π discontinuous?
Suppose we experiment with an Atwood Machine consisting of two masses m
and 2m connected by an inextensible non-slip string running over a pulley of
radius a and mass 4m, as shown below.
) Briefly discuss why no work is done by the forces of constraint. (5)
(d) What is the total energy of the system? (2)
(e) Find the acceleration dv/dt of the blocks.
