3. Let t be a real number. Prove tn lim = 0. n-x n!

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A:

Q: a' + b' + c\!/r 9" - Vabe. Geometric mean Prove that lim 3 where a, b, and c are positive real…

A: Let Take natural logarithm on both sides.

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A:

Q: Find the limit

A:

Q: Find the mass M and center of mass x of the linear wire covering the given interval and having the…

A: The density of the given wire is δx=7+5x4, -4≤x≤4. We have to find the mass and center of mass of…

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A:

Q: Express O(n² + 500n) as:

A: This is a problem of complexity.

Q: 2. Prove that a. lim, b. lim,1

A:

Q: 2 2 - Let S₁ = 3x₁² x₁ + 3x₂² Ax₂ +...+ 3x² Ax, where the Ax;, fill out the x-interval from x = -2…

A: Given that Sn=3x12∆x1+3x22∆x2+...+3xn2∆xn, where the ∆xi fill out the x-interval from x=-2 to x=6…

Q: 23. lim 1 /n² +1

A: To prove: limn→∞nn2+1=1

Q: Evaluate the limit.

A: Given:                     limx→∞e4x-1-4xx2 Dividing the numerator by highest power denominator:…

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A:

Q: Find lim (a + 2ar + 3ar² + n→∞ .. +nar"-¹) where |r|< 1.

A:

Q: Find the limit as n -> infinity of ln((9n-7)/(6n+4))?

A:

Q: 1 Assume that lim xn +oo. Prove that lim n-00 n +o0. n-00 k=1

A: Given limn→∞xn=+∞

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: 1 Ask for the answer to lim x (1 – e * ).

A:

Q: Compute lim 0 tan-(5x) 5 25 undefined 1 25

A: