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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 )
two sides of an equilateral triangle have lengths 3x-1 and 3x-1. Which of 27-x or 2x-4 could be the length of the third side?
y=f(a^x) and f(sinx)=lnx find dy/dx? Solution) dy/dx exist only when 0 1 as the function y = f(a^x) itself does not exist.
Hypothesis Testing Definition of Hypothesis Testing - A hypothesis is a claim or an opinion about an issue or item. Hence it has to be tested statistically in order to esta
Finding Absolute Extrema of f(x) on [a,b] 0. Confirm that the function is continuous on the interval [a,b]. 1. Determine all critical points of f(x) which are in the inte
If α,β are the zeros of a Quadratic polynomial such that α + β = 24, α - β = 8. Find a Quadratic polynomial having α and β as its zeros.
1+2+3+78+980
What is 124 out of 300 in percent ?
Example Evaluate following limits. Solution Here our first thought is probably to just "plug" infinity into the polynomial & "evaluate" every term to finds out the
A medical survey was conducted in order to establish the proportion of the population which was infected along with cancer. The results indicated that 40 percent of the population
Differentiate following functions. (a) f ( x ) = 2 x 5 cosh x (b) h (t ) = sinh t / t + 1 Solution (a) f ′ ( x ) = 10x 4 cosh x + 2x 5 sinh x (b) h′ (t ) = (t
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