Graphs of Trigonometric Functions. Below are the graphs of the six trigonometric functions: sine, cosine, tangent, cosecant, secant, and cotangent. Explore the amplitude, period, and phase shift by examining the graphs of various trigonometric functions. Graph of y = sin x. Graph of y = sin ax. Graph of y = cos x. Graph of y […]
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Category: IB/Cambridge
First fundamental Theorem of Calculus
Fundamental Theorem of Calculus. If we define an area function, F (x), as the area under the curve y=f (t) from t=0 to t=x, then the area function in this case is F (x)=c∗x. We would like to be able to evaluate more integrals with a process like this, The fundamental theorem of calculus tells us that if f […]
Second fundamental Theorem of Calculus
Then F ( x) is an antiderivative of f ( x )—that is, F ‘( x) = f ( x) for all x in I. That business about the interval I is to make sure we only get limits of integration that are are reasonable for your function. Some things that wouldn’t be reasonable: Choosing […]
Average value theorem
Average values theorem of the function f(x) on the interval [a,b] is the integral of the function. Hence it give exact of a function on an interval. Also in decimal within interval. Average value
Trapezoidal Rule-2
trapezium rules is a way of estimating the area under a curve. so the trapezium rule gives a method of estimating integrals. Due to this we get approximate answer . Also we can get area using integration. trapezium rule
Trapezoidal Rule
The trapezium rules is a way of estimating the area under a curve. so the trapezium rule gives a method of estimating integrals. Due to this we get approximate answer . Also we can get area using integration. trapezium Rule
Approximating area under the curve
Approximate area of under a curve. Compute left, right, and midpoint Hence Riemann sums use with n rectangles are computed. Due to the this it approximate area. Approximate area under
Riemann sum( table)
A Riemann sums is an approximation of a region’s area. It obtained by adding up the areas of multiple simplified slices of the region. It is applied in calculus to determine the area of a region. Hence it give approximate area of region. It is also give right and left sum. Riemann sum
Probability
Probabilities is the measure of the likelihood that an event will occur. A number between zero and one that shows how likely a certain event. Another probability of event A is the number of ways event A can occur divided by the total number of possible outcomes. Also expressed by the ratio of the number of actual occurrences […]
Mathematical Induction (Divisibility)
Mathematical induction is a special way of proving things. It has only 2 steps: Step 1. Show it is true for the first one Step 2. Show that if any one is true then the next one is true. Mathematical induction
