• The graph of y = F (x) shown in Fig. 1.1 is the graph of the corresponding parametric equations x = f (t), y = g (t). It's called a parametric curve. The parametric curve is the path of the motion of the object, because each point (x, y) on it is a position (x, y) of the object in the plane at time t, where x = f (t) and y = g (t).
  • The function $\ds y=x^{2/3}$ does not have a tangent line at 0, but unlike the absolute value function it can be said to have a single direction: as we approach 0 from either side the tangent line becomes closer and closer to a vertical line; the curve is vertical at 0.
  • Just to be sure the function does not diverge on the interval check where the roots of the denominator are. But note the following: Ax2 + Bx +C = 1 x2 + (1) x + 1 )B2 4AC = 1 4 1 1 = 3 < 0 So the roots are imaginary and the function does not diverge on the interval. Now to find the critical points of the function. f0(x) = (x2 x + 1) x(2x 1 ...
  • A. In NCERT solutions for class 12 maths chapter 6, you will learn the application of derivatives, finding rate of change, show increasing/decreasing in whole domain, in intervals, find intervals of increasing/decreasing, Rolle’s theorem, Lagrange’s Mean Value theorem, finding slope of tangent/normal, point when tangent is parallel/ perpendicular, when point and curve is known, when slope ...
  • f is said to be decreasing on an interval I if for all x in I, f (x 1) > f (x 2) whenever x 1 < x 2. A function is monotonic on an interval I if it is only increasing or only decreasing on I. The derivative can help us determine whether a function is increasing or decreasing on an interval. This knowledge will later allow us to sketch rough ...
  • On the interval [a,B] we can integrate (this is the assumption of our definition), we can therefore determine the area under the graph of f from a to B. If we want to get some idea about the area under the graph of f all the way to b , the natural approach is to take the areas that we obtained for different B 's and ask what happens to them ...
  • Directions: Upload your work in eCampus. Show all your work neatly and concisely and Box your nal answer. You will be graded not merely on the nal answer, but also on the quality and correct-ness of the work leading up to it. 1.(6 points) Evaluate lim x!ˇ sin7xcsc5x Sol. The expression sin7xcsc5x= sin7x sin5x is of the form 0 0 as x!ˇ.
  • A function for which every element of the range of the function corresponds to exactly one element of the domain. One-to-one is often written 1-1. One-to-one is often written 1-1. Note: y = f ( x ) is a function if it passes the vertical line test .

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(d) The average speed in the interval 0 s to 10 s is the same as the average speed in the interval 10 s to 20 s. Explanation: (a) The slope of the v–t graph gives the acceleration. For the given graph, the slope is constant. So, acceleration is constant. (b) From 0 to 10 seconds, velocity is in positive direction and then in negative direction.
A function is increasing where from left to right, the y-value INCREASES, and decreases where the y-values DECREASE: a) the function is positive for x >1. b) the function is negative for x < 1. c) the function is never increasing. d) the function is decreasing for all x, where x =/= 1 (since the function is undefined at 1).

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$\begingroup$ The Icelandic term endanlegt fall is defined this way in a dictionary, and endanlegt means finite and fall means function. But that dictionary states that the English translation of the term is logic function (which I've never seen used in that meaning). $\endgroup$ – Bjartur Thorlacius Aug 21 at 11:18
Graphs of functions with different amplitudes and periods. Periodic Function A function f is said to be periodic if f(x + P) = f(x) for all values of x. The constant P is called the period, and is required to be positive. A function with period P will repeat on intervals of length P, and these intervals are sometimes also referred as periods.

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In this section we will discuss what the first derivative of a function can tell us about the graph of a function. The first derivative will allow us to identify the relative (or local) minimum and maximum values of a function and where a function will be increasing and decreasing. We will also give the First Derivative test which will allow us to classify critical points as relative minimums ...
Ho to find function the Superimum of function (sup f(x) ), for example, I want to find the supremum of the exponential distribution i.e. f(x)=lambda*exp(-lambda*x)