174 Using the Mean Value Formula for Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 Calculating Arclength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
I think your confused about what a “limit” really means. When I saylimx→1x2−1x−1=2limx→1x2−1x−1=2, I mean to sayf(x)=x2−1x−1f(x)=x2−1x−1gets (arbitrarily) closer to22whenxxgetscloserto11(but is not exactly11). As an example of what I mean, ...
What does this step in the epsilon delta proof for limit of following function mean? Ask Question Asked today Modified today Viewed 18 times This question shows research effort; it is useful and clear -1 Save this question. Show activity on this post. I ca...
2. What are Derivatives? Derivatives are defined as the rate of change of a function or a dependent variable with respect to the arguments or the independent variables. 3. What do you mean by continuity of a function? Continuity is defined as the property of a function that the graph of ...
An indefinite integral does not have a specific boundary, i.e. no upper and lower limit is defined. Thus the integration value is always accompanied by a constant value (C). It is denoted as: \(\begin{array}{l}\int f(x).dx = F(x) + C\end{array} \) ...
What Does Differentiable Mean in Calculus? Differentiability is another concept that is relevant to the application of calculus. Functions can be differentiable or non-differentiable. When a function is differentiable, there is a defined derivative at a specific point. This means that the slope of ...
“Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,— social, political, moral,—on which the ...
But what does it mean? Let's say I gave you a magic newspaper that listed the daily stock market changes for the next few years (+1% Monday, -2% Tuesday...). What could you do? Well, you'd apply the changes one-by-one, plot out future prices, and buy low / sell high to bui...
Mean Value Theorem The instantaneous rate of change will equal the mean rate of change somewhere in the interval. Or, the tangent line will be parallel to the secant line. Horizontal Asymptote Reciprocal function D: (-∞,+∞) x can't be zeroR: (-∞,+∞) y can't be zero Square root...
we saw the value of extending Taylor.s theorem to infinitely differentiable functions.�This would mean we would have an infinite series with infinite derivatives. The only way to prove that such a series could be written and would hold true for any value of x was by taking the limit of...