4/28/2023 0 Comments Fx equation in math![]() In other words, for every point on the graph of f(x)=e^x, the slope of the tangent is equal to the y-value of tangent point. 0000000000000000000001.but you will find that as h gets closer to zero, the value of the limit gets more accurate).Į^x times lim h->0 (e^0.0001 - 1)/0.0001 : the value of the limit is 1į'(x)= e^ x : this proves that the derivative (general slope formula) of f(x)= e^x is e^x, which is the function itself. Thus, move the e^x in front of the lim.Į^x times lim h->0 (e^h - 1)/h : approximate the value of the limit by picking a number very close to zero to input into 'h' value. Lim h->0 /h : the coefficient, e^x does not depend on the denominator it can be interpreted as (e^x)/1 times (e^h - 1)/h. If you did not recognize this operation, you can set e^x = a Lim h->0 /h : factor out e^x, since this is the common factor. Thus, e^(x h) can be separated as e^x times e^h, since multiplying the two bases with the same exponent simply means to add the exponents together. Lim h->0 (e^x times e^h - e^x)/h : bare with me, I know it's difficult to illustrate this but remind yourself that a^(b c) is equivalent to a^b times a^c, as long as the base is the same, according the the exponential laws. Now that we have established the terms for the limit notation, we can continue: Let's prove it using the general limit notation!įirst, plug in (x) and (x h) into the exponent. As noted by this video, the general formula for this equation is the equation itself: e^x. See Figure 2-3 for a summary of interval notation.F(x)=e^x : this will be our original equation that we want to differentiate to achieve the general formula.
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