c) Now compute the numerical value of the definite integral by determining the limit of the summation from b) as n approaches infinity. n (2 + 6x) dx = lim f(x;)Ax = %3D 3 i=1

Q: Use the limit definition of definite integral in the form of f(æ) dæ = lim {(#:)Ax, i=1 6 - a and r;…

A:

Q: (b) With the help of Sandwich theorem (or Squeeze theorem), show that lim (2 √√x - 1)" = x² for x ≥…

A: By using Sandwich theorem,  we have to show that ;   limn→∞2xn-1n = x2  for x≥1

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Q: Express the limit as a definite integral on the given interval. xi* (x)² +9 lim n→ co -AX, [1, 3] dx

A: limn→∞∑i=1nxi*xi*2+9∆x,    1,3

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A: Explanation of the answer is as follows

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Q: Please

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Q: 9. lim 15 1 + (i/n)6

A:

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A: The given sequence Cnn=1∞ is defined as ; Cn = fxn f'xn-1fxn-1 f'xn  and  f'(α) ≠ 0  and xn → α…

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A: Given: f(x)=1x−2−4x−4Estimate:limx→4f(x)=?Graphically  and  Numericallly

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Q: lim [ln(1 + x²) − ln(1 + x)] - X

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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.