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Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
which ratio is largar. 1. 15:16 or 24:25
Solving Trig Equations : Here we will discuss on solving trig equations. It is something which you will be asked to do on a fairly regular basis in my class. Let's just see the
prove that the composition of two simple harmonic of the same period and in the same straight line is also a simple harmonic motion of the same period.
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
Consider the following interpolation problem: Find a quadratic polynomial p(x) such that p(x0) = y0 p’(x1) = y’1 , p(x2) = y2 where x0 is different from x2 and y0, y’1 , y2 a
Total Contribution per Year for next 10yeras =$1000+$800 =$1800 So Total Future fund Vaule =$1800*(1+1.073+power(1.073,2)+ power(1.073,2)+ power(1.073,3)+ power(1.073,4)+ power
Illustration 1 In a described exam the scores for 10 students were given as: Student Mark (x) |x-x¯| A 60
y=f(a^x) and f(sinx)=lnx find dy/dx Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1) but f(sinx) = lnx implies f(x) = ln(arcsinx) hence f''(x) = (1/arcsinx) (1/ ( ( 1-x
Example : Determine the Taylor series for f(x) = e x about x=0. Solution It is probably one of the easiest functions to get the Taylor series for. We just require recallin
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