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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 )
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Parallel to the line specified by 10 y + 3x= -2 In this case the new line is to be parallel to the line given by 10 y ? 3x ? -2 and so it have to have the similar slope as this
sin (cot -1 {cos (tan -1 x)}) tan -1 x = A => tan A =x sec A = √(1+x 2 ) ==> cos A = 1/√(1+x 2 ) so A = cos -1 (1/√(1+x 2 )) sin (cot -1 {cos (tan -1 x)}) = s
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Simultaneous equations by substitution: Solve the subsequent simultaneous equations by substitution. 3x + 4y = 6 5x + 3y = -1 Solution: Solve for x: 3x = 6
Let's recall how do to do this with a rapid number example. 5/6 - 3/4 In this case we required a common denominator & reme
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