-1 -1 Differentiate xe 1 2 and hence integrate 2 dx.

Q: xy' - y = = x tan Y 18

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Q: Let xn -> 0 and (yn) be bounded. Prove xnyn -> 0.

A: A sequence is bounded if it is bounded above and below, that is to say, if there is a number, k,…

Q: Express the limit as a definite integral on the given interval. [9(x†)3 – 4xj]Ax, [2,9] lim n- 00 i…

A: Express the limit as a definite integral on the given interval.

Q: use a table to estimate the limit of g(x)= sin2x/3x as x approaches zero. show how to plug in…

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Q: Express the limit as a definite integral: limn→∞ sec² (1) ΣΩ .) π k=0 4n Of sec(πx) dx O T O Sot…

A: To express the following limit as a definite integral.

Q: True False Suppose f(x) is continuous everywhere. Must f(x) attain an absolute maximum somewhere on…

A: Extreme value theorem states that if f(x) is continuous on closed interval I, then f(x) attains…

Q: Suppose that ƒ is continuous in [0,1] and that f(x) E [0, 1] for all x. Show that f(x) = x for some…

A: Given that f:0,1→0,1 is continuous on 0,1. To show fx=x for some x∈0,1

Q: Find the limits

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Q: x+2a, if x<1 What value for a would makef (x)continuous everywhere? Let f(x)= (ax? +7x-4, if x21

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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

Q: Express the limit as a definite integral on the given interval. [3(x)³ - 7x*]4x, 2 lim i = 1 dx…

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Q: 1. The function(x)=x-1 has a discontinuity, say where and justify the response. Classify the…

A: Given f(x)=x4-1x-1. to check the discontinuity of f(x).

Q: Find  limit x 0  1/x^2if it exists.

A: We find the limit numerically

Q: for z+ - and Let f(z) = for z or (a) Show that is continuous at -n/2.

A: a) When x≠-π2 limx→-π2cosxx2-π24

Q: Express as a definite integral the limit as x approaches infinite of 1/n[(1/n)^2 + (2/n)^2 +...+…

A: Step 1:

Q: Find the antiderivative of the improper interval xe-x^2 from negative infinity to positive infinity

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Q: H(3)=6 and the limit as x approaches 3 of H(x) is 6. Mustache be continuous at (3,6)? State why.

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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.