Precalculus
... Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of ...
... Define and graph trigonometric functions using domain, range, intercepts, period, amplitude, phase shift, vertical shift, and asymptotes with and without the use of ...
Lecture 1:
... (negative, positive, fractions, decimals, zero, whatever), and the function will work, but it won't always produce real numbers (plug in 2, and you'll get a complex number). So if we want to restrict the range to be only real numbers, we'd have to restrict the domain (in this case, it has to be grea ...
... (negative, positive, fractions, decimals, zero, whatever), and the function will work, but it won't always produce real numbers (plug in 2, and you'll get a complex number). So if we want to restrict the range to be only real numbers, we'd have to restrict the domain (in this case, it has to be grea ...
MTH/STA 561 GAMMA DISTRIBUTION, CHI SQUARE
... Proof Let y = t (or t = y= ). Then dy = dt (or dt = dy= ). Also, y ! 1 as t ! 1 and y ! 0 as t ! 0. Thus, ...
... Proof Let y = t (or t = y= ). Then dy = dt (or dt = dy= ). Also, y ! 1 as t ! 1 and y ! 0 as t ! 0. Thus, ...
Fundamental theorem of calculus
The fundamental theorem of calculus is a theorem that links the concept of the derivative of a function with the concept of the function's integral.The first part of the theorem, sometimes called the first fundamental theorem of calculus, is that the definite integration of a function is related to its antiderivative, and can be reversed by differentiation. This part of the theorem is also important because it guarantees the existence of antiderivatives for continuous functions.The second part of the theorem, sometimes called the second fundamental theorem of calculus, is that the definite integral of a function can be computed by using any one of its infinitely-many antiderivatives. This part of the theorem has key practical applications because it markedly simplifies the computation of definite integrals.