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Some Definitions of e
1.
2. e is the unique +ve number for which
3.
The second one is the significant one for us since that limit is exactly the limit which we're working with above. Thus, this definition leads to the following fact,
Fact 1
For the natural exponential function, f ( x ) = ex we have
Hence, provided we are using the natural exponential function we obtain the following.
f ( x )= ex ⇒ f ′ ( x ) = ex
At this instance we're missing some knowledge that will let us to simply get the derivative for a general function. We will be able to show that eventually for a general exponential function we have,
f ( x ) = a x ⇒ f ′ ( x ) = a x ln ( a )
Exponential and Logarithm Equations : In this section we'll learn solving equations along with exponential functions or logarithms in them. We'll begin with equations which invol
Limit Comparison Test Assume that we have two series ∑a n and ∑b n with a n , b n ≥ 0 for all n. Determine, If c is positive (i.e. c > 0 ) and is finite (i.e. c
Generate a 1000 vertex graph adding edges randomly one at a time. How many edges are added before all isolated vertices disappear? Try the experiment enough times to determine ho
Formulas of Surface Area - Applications of integrals S = ∫ 2Πyds rotation about x-axis S = ∫ 2Πxds rotation about y-axis Where, ds = √ 1 + (1+ (dy /
find middle term [2a-a2/4]9
3x2 +7x +4
Unit Vector and Zero Vectors Unit Vector Any vector along with magnitude of 1, that is || u → || = 1, is called a unit vector. Zero Vectors The vector w → = (
X-intercept If an intercept crosses the x-axis we will call it as x-intercept . Y-intercept Similar, if an intercept crosses the y-axis we will call it as a y-inter
what is the consective sum for 2+3
Under this section we're going to go back and revisit the concept of modeling only now we're going to look at this in light of the fact as we now understand how to solve systems of
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