Determine whether the sequence converges or diverges. If it converges, find the limit. (If the sequence diverges, lim Justify your answer. O Use L'Hopital's Rule to find an equivalent limit that does not have an indeterminate form. Rewrite the expression as a quotient and use the Quotient Rule. O Use the Squeeze Theorem by comparing to the sequence b, = (1)e-S". Use the Power Rule by finding a common exponent of the products.

Q: Find the one-sided limit (if it exists).

A: We first factor the denominator

Q: e2x -1 Use L’Hopital's Rule to find the limit. lim

A:

Q: Find the limit. Use l'Hospital's Rule if appropriate. lim0 * 3* 3* -1

A:

Q: Find the limit as x--> ∞ lim In x2 O 2x 00 8.

A:

Q: Evaluate the limit.

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

Q: lim (√n²+ n-n)

A:

Q: Q5. Find the general solution to the following set of ODES. y₁ = y₁ + y2 + sint y₂ = 4y1 + y2

A: Here we firstly, find the value of y1 and then by putting the value of y1 in equation (i) we find…

Q: 1/m 12x-141 *ㅋㅋ X-7

A: We have to check the limit of the given function at 7- and 7+

Q: Use continuity to evaluate the limit. 16 + Vx lim 16 + x

A:

Q: Find the limit. lim e8/(5 - x)

A: Given,  limx→5+e85-x  We have to find the limit.

Q: Find the limit if it exists. Lim, 19 (x)

A:

Q: n! - (n+ 1)" lím (1+m) · (2+ m) ·. .· (n+ m)

A: Given expression is    limn→∞n!n+1m1+m2+m...n+m We have to find limit when m=2 and m=3.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.