Using e – N description to prove that lim = 2. n2 +1

Q: 3 find the limit if it exists .If it do esn't exist, explain why. lim 13+x| X-> -3 2(34+X)

A:

Q: 5. a) Explain why lim vx-3 does not exist. b) What about lim V(x 3)2 ?

A:

Q: 4. Evaluate lim [In(2+x)-In(1+2.x)] using Calculus 1 limit techniques. Show all steps to justify…

A: To evaluate: limx→∞ln2+x-ln1+2x Solution: We know that, lna-lnb=lnab Therefore,…

Q: Determine the law limit applied in solving lim 3 = 3. t-1 A. Limit of an identity B. Limit of a root…

A: Solution ) limit of a constant  limx→a b = b  limit of x tending to any value is value of the…

Q: lim(8x + 16) = 24 Use the epsilon-delta definition of limit to prove that æ→1

A: Let's find.

Q: xCosx-In(1+x)] х-Тапх, limx-ol limx-o[ a) х-Sinx c)

A: a ) given limit is as below:

Q: 21: The final value of :* lim (In(x))?

A:

Q: 2n +1 a) Using the definition, show that lim n00 3n +4 3

A: Given,           limn→∞2n+13n+4=23

Q: 19. lim (-1)"+' (") does not exist. n00

A: Given  The limit is limn→∞(-1)n+1n-1n

Q: find the limit or explain why it does not exist

A: To find the limit.

Q: Prove that lim š +1) = 3 using the e-8-definition.

A:

Q: Determine the limit: lim 1+n-'sin3(n) А. С. -1 1, B.

A: Introduction: When we deal with sine or cosine function in limits, we follow the inequality sinx≤1.…

Q: 2. Find the limit 2 - 3" lim →∞ 3+ 4

A:

Q: lim (In x) x→0+

A: Given,          limx→0+lnx

Q: lim In(x+3) 4) 1

A: Evaluate :     limx→∞ln3xlnx+3

Q: Find the limit.

A:

Q: Using e – N description to prove that lim - = 0.

A:

Q: 17. If lim- X- 200 – 4n + kn² then k =

A: Given

Q: 40. Prove that lim Vx esin(7/x) = 0. 41-46 Find the limit, if it exists. If the lim explain why.

A:

Q: tan(x) Q1: limx¬n X-n is

A:

Q: 5. If f(a) is undefined, then the lim S(x)does not exist. True or False? Explain.

A:

Q: 1. Use the e-definition to show that lim 1)- 3. n+1

A:

Q: 2t – 1 Evaluate lim,, tan-1, e> - t - 1

A:

Q: Find the limit.

A: Given: The function is f(x)=lnx2-9 To find: we have to find the limit at x→3+

Q: 1:3.5. - - (2n-1) now lim lim (n+1)! 1.3. 5-- - (2n-1)

A: Step1: Here to calculate the limit we value we have used the limit ratio test , where we the given…

Q: (a) Using only the e,8-definition of limit, prove that 1 lim x--1 x2 (b) Let n be a fixed positive…

A:

Q: Show that lim (1 – 2²)"dr 0, n 00 0,

A: To show limn→∞∫01(1-x2)ndx=0 without attempting direct intergral.

Q: EXAMPLES. Observe that iz +3 lim z→-1 z +1 z +1 =D0 since lim %3D z→-1 iz + 3

A: Now, limz→-1z+1iz+3=-1+1i(1)+3                 =0-1+3                 =0…

Q: 5. Evaluate the limits using any of the methods you know. Show your work. In(1+4x) c. lim tan 2x

A: find the limit

Q: 6n + 2 3. n→∞ 2n + 1 3. Using the definition (i.e. N, E), prove that lim

A:

Q: 3n³-4n+1 Find lim,00 . (show all necessary en details)

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x…

A:

Q: ure E-S theorem to prove the following lim (9x+5) = - 32. x→3

A: Here we will evaluate the required value.

Q: 5- x 37. lim In

A:

Q: 8. Find lim x² In x x→0+

A:

Q: Prove that lim Vr = 2 using the e-d-definition. Hint: VI - 2 = x - 4 %3D VI+2°

A:

Q: Find the limit.

A: Given,

Q: Find the limit. lim sec x lim sec x= (Type an integer or a simplified fraction.)

A: Solve the given problem

Q: 3. lim- im:-) (x+r)²

A: Given: limt→02t5(x+t)2-5x2

Q: 6 Find the value of a such that 2x2 - ах — 14 lim х-1 х2 — 2х — 3 exists, What is the value of the…

A: The limit of a function at a point 'a' in its domain is the value that the function approaches as…

Q: 33. Verify that another possible choice of & for showing that limx-3 x? = 9 in Example 4 is 8 =…

A: Guessing a value for δ. Let ε>0 be given. We have to find the a number δ>0 other than example…

Q: Compute the limit below. Justify your answer. (You will receive no credit without showing work and…

A: We have given the limit- limx→52x2-9x-57x-35 We have to compute the value of the given function.

Q: Prove using the definition of a limit. lim x→2^− (1/((x^2) − 4)= +∞)

A: Prove that   limx→2-1x2-4=∞

Q: Find lim I -4 2+1 1 lim z - -4 +1 Show your work and explain, in your own words, how you arrived at…

A:

Q: Lim ģ G メ-ム

A: We have to use L' Hospitals rule ,if we get any indeterminate forms (00,0×∞, ∞∞,∞,-∞) when we…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.