The area function for the function f depicted in the graph below is given by A(z) = S f(t) dt. The vertical position of this function is determined by our choice of the lower limit a. 2.5 f 1.5 1 0.5 -0.5 0.5 1.5 2 2.5 -0.5 -1 When a = 2 we have the following function values for z = 0 and z = 2: О А(0) — 0, A(2) — 2 %3| О А(0) — 2, А(2) — 0 %3D О А(0) — — 2, А(2) — 0 O A(0) = 0, A(2) = -2 None of the above. 2.

Q: Suppose that the values of a smooth function f is known for x=0, 0.3, 0.6 and 1.2. Select the 3-…

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Q: Let y(t) be the solution of the initial value problem y" – y/ – 20y = 0, y(0) = 2, y'(0) = B.

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Q: E. Set up the limit definition for finding the derivative of y = sin x.

A: Givne that  y=sinx  From the limit definition find the derivative of y=sinx

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.