01-02-2013, 11:25 AM
TECHNICAL MATHEMATICS 1I
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Differentiation
Define the derivative of a function y = f(x) as limit y
x->0 x
Find the derivatives of xn, Sinx, and Cosx from first principles
State the rules of differentiation
1) Sum or difference
2) Product
3) Quotient
Find derivatives of ex and log x. State all the fundamental formulae
Apply the rules and differentiate simple functions of the type
Applications of Differentiation
State geometrical meaning of derivatives
Find the slope of the curve
y= x2-3x + 2 at (3,2)
y = tan x at x = /3
Find the equation of the tangent and normal to the semi
circle y = 25-x² at (4,3) on it
Solve problems of the type: The radius of a circular plate is increasing
in length at 0.1 cm per second. What is the rate at which the area is
increasing when the radius is 12 cm.
Solve problems of the type: A spherical balloon is inflated with air such
that its volume increases at the rate 5.c.c per second. Find the rate at
which its curved surface is increasing when its radius is 7 cm.
Solve problems of the type: The displacement ‘S’ in time ‘t’ is given by S =
2/3t+ Cost at t = /4; find the velocity and acceleration
State the conditions for a function
y = f(x) to be (1) increasing (2) decreasing
Apply the concept of derivative to find maxima and minima
Solve the problem of the type:
1) Find the maximum and minimum values of y = x³ – 18 x² + 96 x
2) Prove that a rectangle of fixed perimeter has its maximum area when
it becomes a square.