28. Let (п — 1)2 12 S, 22 ... n? To calculate lim,2 S,, show that Sn + ... + п п and interpret S, as an approximating sum of the integral x²dx. (Hint: Partition [0, 1] into n intervals of equal length and write out the approximating sum for inscribed rectangles.)

Q: EX/ show that im Cosy-1

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A:

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A: To prove that                limn→∞nn2n!=0

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A:

Q: 2x² +3x+1 10.) lim x00 3x2 -5x+2

A: We can evaluate the limit as below

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A: To find the lim sup and lim inf of the given sequence An .

Q: 1 lim E n→ 00 i=1 'n² + i?

A:

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A:

Q: 80 F七im 十 2 thenE enthjeonverges

A:

Q: lim,-«G)* + x²+4 ()* limx--o %D 3x +1 a. -1 1 c. -3 Od. 3.

A: Given, limx→-∞53x+9x2+43x+1  We have to evaluate the limit.

Q: Determine the 3z 1 2x 1 2x 5 lim 00 O 00 2/4

A:

Q: & Prove that lim I = 2 using the e-d-definition. Hint: Vr %3D

A: Given: To explain the given statement as follows, Here, prove that limx→4 x = 2.

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A: We can find the limit of an expression by applying the limit point to the variable in the expression…

Q: Zim x²-3x³ +5 X-700 X²4 +12X10+ 5

A:

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A: If you like the solution then please give it a thumbs up.... The Answer is:           Result :   =…

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A: We have ,  limt→1n(t)=t3+1, t<112(t+1), t⩾1 we have to find the limit.

Q: 1-x c) lim- x1 1-Vx 121 sin x d) lim (Hint: Use a calculator to make a table.)

A: c) limx→11-x1-xd) limx→0sin xx

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A:

Q: 79. lim x→1 In x

A: Givenlimx→1- xln x

Q: Use algebra to evaluate the following limits. x-6 lim a) x6 3x² - 12x - 36 lim b) x-0 x² + 2x² + 7x…

A: Make the factor or cancel the term for finding the limits .

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

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Q: ex+2x ? x-00 ex-Inx What is the value of lim O A) 1 -2 D) E) 0 B)

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A: Apply exponent rule