3.) lim r/z2

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

A: The limit of the function can be found by the substitution of the point and by the help of the…

Q: Using L'Hospitals Rule, what is limx->infinity (1+3/x)x

A: Let y= (1+3/x)^xApply ln on both sides.

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

A:

Q: Find the limit. Use a graphing utility to verify your result.

A: We first rationalize the numerator

Q: Find the limit. 3 lim ( 1 %3D

A: The given limit is of the form limx→∞f(x)g(x) which is 1∞, and the solution of this limit is:…

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

A:

Q: Find the limit by rewriting the fraction first. ху — Зу - 7х + 21 lim х - 3 (х,у)— (3,8) x#3 ху — Зу…

A:

Q: Exercise To Try 3 Determine the limits lim 2-a X→1 (x–1)2

A:

Q: iz2-z- lim- z²-1 z-a

A: We have to use polar substitution.

Q: Using the ε−δ− definition of limit, show that limx→3(3x−2)=7.

A: Given:

Q: 18.L. Define what is meant by lim sup f = L, lim inf f : = -- ¤. %3D

A: Given that limx→+∞sup f=L, limx→+∞in f=-∞ The meaning for the limx→+∞sup f=L is, There exist M>0…

Q: 2. Find lim (√x + 2 = √2).

A:

Q: 8. Compute, justifying, lim5 x2 +9 - V2 x² + 9 )/ x² .

A:

Q: iz?-z- lim- z2-1 i o -i O 1 0 -1 0

A: Calculation/ Explanation : Let  A = limz→∞i z2 - zz2 -1 Divide numerator and denominator with z2 we…

Q: Find the value of lim sec 3. 2 Select your answer. 2/3 3 3 2/3 +3 3 2/3 – 3 3. 2/3 3 3

A:

Q: Find the limit. (Hint: Treat the expression as a fraction whose denominator is 1, and rationalize…

A: given

Q: Once you know limx →a+ ƒ(x) and limx →a- ƒ(x) at an interior point of the domain of ƒ, do you then…

A: If the left and the right-hand limits of a point are equal then the limit at the point exists. So,…

Q: Prove, using the formal definition, that limx→ 8 [(x)^1/3 = 2.]

A: The definition of limit is  limn→∞an=l foe each ε>0, there is a positive integer N such that…

Q: Using L'Hospitals Rule, what is limx->0+ (xsqrt(x))

A: We need to find the value of the limit using L’Hospital’s rule,

Q: Find (a) limxS400+ :x; and (b) limxS400- :x;; then use limit definitions to verify your findings.…

A: (a) Given: limx→400+x  ……1

Q: lim,→ 0 + (5xtan(2x))

A:

Q: 2-limx-o 6x cot3x

A:

Q: Vx² +9 – 3 lim 2

A: Given  limx→0x2+9-3x =limx→0 x2+9-3x2+9+3xx2+9+3         multiplying x2+9+3 on numerator and…

Q: lim (x² + 2)sech>

A:

Q: 2х-п lim =? COSX 2

A: We can use differential calculus to find the solution. When we directly apply the limit we get an…

Q: Calculate the limit. lim (-1)"n? (Give an exact answer Use symbolic nototi

A:

Q: secies to find lim use

A:

Q: lim (x³ + 4x² + 4x – 1) = -1, a-2 1 lim - = 1.

A: Given,

Q: Using Squeeze Theorem, show that lim x* cos-

A: Squeeze theorem

Q: Using L'Hospitals Rule, what is limx->infinity (ex + x)(9/x)

A: Given information.

Q: lim 1418 r = ∞ zª

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: Given: limx→0 xx=1 To determine: Given statement is true or false.

Q: 3 Find limx-2 Using a table. х-2

A:

Q: Find lim (1+ D (if it exists)

A: We have to find the value of the given limit: limx→∞1+1xx Here given limit is in 1∞ indeterminate…

Q: Show that lim +7.6' 3D7 3^+6^

A: Consider the given limit,…

Q: Find the limit. (Hint: Treat the expression as a fraction whose denominator is 1, and rationalize…

A:

Q: x²y + x³y² lim (x,y)-(-2,1) x² + y2

A:

Q: 2x2-ху-у? x²-y² Evaluate lim (х.у) - (1,1) (2) 3. 2

A:

Q: Find the limit 1 1 Find limX+3

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

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

A:

Q: Why does lim sec x = – o? How is this related the triangle in the drawing below? Explain. Adjacent

A:

Q: Lim xsinx

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: What is lim e7-1 Provide your answer below:

A: The objective is to find the limit.

Q: Use the comparison test to show that lim ootu 6n +n³ 5n - n³

A:

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: Using direct substitution, what is lim²+6z_5, Z-2 223 O 1 O 1 O does not exist

A: We have to find    limx→2x2+6x-5x2-3

Q: 2. Letgx-15x+2,-2,x+2, x0. Does the limx - Og(x) exist? If yes, give its value. If not, why?

A:

Q: 1 (a) lim I+5- x – 5

A: that is on puting x=5 from the left we get  the limit= -inf

Q: ® lim inf of snaG)"(-+;) is ?

A: