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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 )
A round balloon of radius 'a' subtends an angle θ at the eye of the observer while the angle of elevation of its centre is Φ.Prove that the height of the center of the balloon is a
sin3θ = cos2θ find the most general values of θ satisfying the equatios? sinax + cosbx = 0 solve ? Solution) sin (3x) = sin(2x + x) = sin(2x)cos(x) + cos(2x)sin(x) = 2sin(x)cos(
draw a line OX=10CM and construct an angle xoy = 60. (b)bisect the angle xoy and mark a point A on the bisector so that OA = 7cm
Explain Linear Equations ? Set of ordered pairs of numbers A set is an undefined term and we describe it as a "well defined" collection. We use the symbol "{ }" to denote "a se
teach me how to o times 7s
Particular to General : When I say 'tail', what do you think of? Do you think of the tail of a horse, or of a monkey? Or do you think of the tail of your pet dog? The tail of
Multiply and divide by root2, then root2/root2(sinx+cosx) = root2(sinx/root2 + cosx/root2) = root2(sinx cos45+cosx sin45) = root2(sin(x+45))
The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find out the width of the rectangle. Let l = the length of the rectangle and let
21-83/4
1 . The probability that a couple will have a child with black hair is 0.6. If this couple has 7 children what is (a) the probability that exactly 3 of these children have bl
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