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1. a) Define differentiation and integration in calculus. Also write down the
differences between them.Β
b) Write down some application of Calculus in CSE.Β
c) Describe geometrical meaning of definite integral with figure.
for a particular function, dy/dx=8x-5. if it is known that when x= 2,y= 8,find y in terms of x
Let g(x) = {(ax^2-b) if x<2, (bx-a) if x>2}
Find a relationship between a and b (that is, solve for a in terms of b or vice versa) So that g(x) is continuous for all of x.
A swimming pool is to be drained for cleaning. The quantity of Q of water (in gallons) in the pool at any given time is a function of the amount of time t (in minutes) which has elapsed since the drain was opened. the function is: Q(t)= 10(20-t)3
find Qβ(t)=
what is the rate of change of the quantity of water in the pool exactly 10 minutes after the drain is opened? (labeled units)
what is the average rate of change of the quantity of water during the first 10 minutes after the drain is open?
how long will it take to drain the pool completely? (labeled units)
If A(u) is a differentiable vector function of u and ||A(u)||=1 , prove that dA/du is perpendicular to A
A 13 ft ladder is leaning against a wall. If the top of the
ladder slips down the wall at a rate of 2 ft/s, how fast will
the foot be moving away from the wall when the top is 5 ft
above the ground?
A town has a population of 5000 and grows at 4% every year the initial population is 5000 find growth model and determine population after 3years
Currently the sowing of wheat is taking place in Pakistan till December, the harvesting season will
begin in March. So, the farmers wants to build a silo in the form of cylinder to keep the wheat inside
the silo after harvesting. For this purpose, they have to built silo of different sizes having 2000 cubic
units and 4000 cubic units. Moreover, the top of the cylinder is hemi-sphere. The cost of construction
of per unit surface area is thrice as great for the hemisphere as it is for the cylindrical sidewall.
Determine the dimensions to be used and cost of construction is to be kept to a minimum. Neglect the
thickness of the silo and waste in construction. Finally, use MATLAB to write a program which will
provide you the optimal dimensions subject to the constraint of cost. The program will take dimensions
of the Silo as input and return the cost and quantity of each size.
1. Find the derivative of the following functions:
a. π(π₯) = tan^-1x+cotx / 5cscx
Β b. π¦=3 βln(2π₯+1)
c. π(π₯)=π₯π^xβsinπ₯ln(5π₯)
If A(u) is a differentiable vector function of u and ||A(u)||=1 , prove that dAdu is perpendicular to A .
