A Riemann sum 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 Sums
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Category: Optional Calculus
Fundamental Theorem of Calculus
FTC(Fundamental theorem 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 is […]
L’ Hopital Rule
L’Hospital rule is simplify evaluation of limits. It does not directly evaluate limits. Therefore L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ Also it solve by differentiation. L’ Hopital’ Rule
L Hopital
L’Hospital rule is simplify evaluation of limits. It does not directly evaluate limits. Therefore L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ Also it solve by differentiation. Hence it is differentiate till indeterminate form. L Hotipal
Differential Equation
A Differential Equation is a function and one or more of its derivatives. Hence it solve by variable seperable and linear differential eq method. Also it solve by homogeneous. Differential Eq
Rolle’s and MVT
Rolle’s Theorem. Then there is a number c such that a<c<b and f′(c)=0. Or, in other words f(x) has a critical point in (a,b). To see the proof of Rolle’s Theorem see the Proofs From Derivative Applications . Roll’s theorem
Piece wise function
Piecewise Functions. A Function Can be in Pieces. We can create functions that behave differently based on the input (x) value. Piece wise function
Power series with Real Coefficient
Power series with Real Coefficients. The exponential function (in blue), and the sum of the first n + 1 terms… Radius of convergence. A power series will converge for some values of the variable x… Operations on power series. Power Series
