Use the ratio test to determine whether n(-5)"| converges or diverges. n! s or (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n 2 3), lim 4nt1 lim (b) Evaluate the limit in the previous part. Enter ool as infinity and -ool as -infinity. If the limit does not exist, enter DNE. lim T 00 (c) By the ratio test, does the series converge, diverge, or is the test inconclusive? Diverges

Q: How would you determine the answer for number 5?

A: Consider the given function,

Q: B. Find the value of the limit. 1. lim *+1)²(x-1) x1 x³+1 x²–4 2. lim x1 x2-3x+2 x²-4 3. lim x2 x-2

A:

Q: Please complete in handwriting. 7

A: Here we have to find the limit by observing the graph.

Q: Find the limit by rewriting the fraction first. У + 64 lim (x.y) (8, - 64) x3y- xy + 64x2 – 64x…

A: Consider,limx,y→8, -64y≠-64, x≠x2y+64x2y-xy+64x2-64xTo find: The limit of the given fraction.

Q: Use algebra to evaluate the limit. [Hint: Multiply by √36+h+6 in numerator and denominator.] Enter…

A:

Q: 10. Evaluate each limit. If the limit does not exist, explain why. a. lim x4 c. lim (x² - 1) b. lim…

A:

Q: 3. Use continuity (direct substitution) to find the limit. 5+ √x x+4√√√5 + x (a) lim (b) lim e²- x-0…

A:

Q: 7. Evaluate the limit: lim . a. 0 b. 1 *--* C. d. T +00

A: Given: limx→ππ

Q: 2. Determine the limit. -5 lim x->2¹ x-2 a. 5 8

A: Here we will find the right hand limit. That is we put x= "2+h"

Q: Complete the table below to identify the limit. Round all numbers to 3 decimal places. x - 5 lim x 5…

A:

Q: 6. Evaluate the limit: lim x+-5+ a. 25 b. 2.5 5x X+ 5* C. c. -25 -co d.

A:

Q: (6,5), (1,4) (-4,2), (6,2) -2 2 4 6 -2 9(1.-2) -4 lim f( x x →-4+ (-) 2.

A: Correct answer is 2.

Q: 4) Determine the limit. lim 1 f(x), where f(x): X + 10 X-- 10-

A: Given, f(x)= 1/(x+10)

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.