Given: lim (x2 + 7x – 5) x→3

Q: Evaluate the limit. Leave results in exact form. V9 + 7r2 lim 11 + 3x

A: This question is based on limits of inf/inf form.

Q: E valuate Dle followneg: lim メーフ+ 7x" – 4x? + 7x - 2 J +- 3 メ 3x° -8x"+ フメー458 -x一5 x3

A:

Q: Find lim x→-∞ ex + 1° (а) — оо (b) ∞ (c) 0 1 (d) 2 Does not exist and has no infinite behavior

A:

Q: What is lim f(z) z→1 9(2) given f(x) = e2" and g(x) 3x2 – 3x + 6 ?

A:

Q: Evaluate the following limits. If needed, enter oo for o and oo for - 0o. V4 + 11x? (a) lim %3D 3+…

A: limx→∞ 4+11x23+10xdividing N and D by xlimx→∞ 4+11x23+10x=limx→∞ 4x2+113x+10limx→∞…

Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: Show that lim (z,y)→(0,0) 4 z - Va² + y? V16 – x² – y? – 2²

A: Show thatlimx,y→0,0z-x2+y24-16-x2-y2-z2=0

Q: Compute the following limits and write your answer to the boxes. lim 4x cot 3x = 5x2 - 10x - 40 lim…

A: From the given problem: a) limx→ 04xcot3x So, we can also write as: limx→ 04xcot3x=4·limx→…

Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

A:

Q: lim 4e-4x lim 5ex - 4 X-4 9x + 7x - 7 lim 2x2 - 2x X- +0

A:

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

Q: ex ) 4. Use the definition of the limit to prove that lim 4x + 2 = 14. %3D x-3

A:

Q: Show that lim (2,v)>(0,0) **+y D0.

A:

Q: Use the precise definition (i.e. the ɛ, d definition) to prove that lim, →1 x2 – 3x + 5 = 3

A:

Q: Find the value of lim f(r), if f(x)%3D 8r +4 3 z-3+ O 12 O 19 O 34 O 35

A:

Q: Find lim (√2-t, et-¹, In(t + 1)) t-0

A:

Q: Prove that lim(x,y)→(1,2) (x2 + 2y) = 5 by using the precise definition

A: ε-δ definition: Limit of function f(x,y) at a point (a,b) is 'L' if for every ε>0 there exist…

Q: If A = lim ("C " C " C_ " C ……." C )m(a+1) then A² is equal to

A:

Q: Use the e-d definition to show that lim /a = 2. a-b (Hint: Vā – V6 =

A:

Q: . Use the sandwich theorem sin x (a) lim Vx 400

A: The given expression is: limx→∞sin xx

Q: Use a u substitution to find Vx – 7 – 2 lim | x-15 x – 15

A:

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: a). Evalieteo lim foca+la -4 X-2 b). f(x){ de?+72, xこ 3x2+3d9x > a Contir at evesy ?

A:

Q: Show that when T(z) = az+b cz+d where (ad - bc ‡ 0), find lim T(z) = ∞ if c = 0. 7-3

A:

Q: b) lim (1 +2x)³A * x=0

A:

Q: Use an appropriate definition to prove the following limits. x³ – 16x* = 1 I+0 r°+ 4x² x +2 V9x2 + 4…

A: This is a problem of limit . Based on the formula and concept we will answer the question.

Q: V9x² + 1 lim x +1

A: Given : limx→∞9x2+1x+1

Q: Find the limit. - V1+x? lim 3x2

A: This is a problem related to limit of the function. Based on using L'Hospital rule we will evaluate…

Q: 2 lim w ln( 1 3w

A: Given:      limω→∞ω ln1-23ω     =limω→∞ln1-23ω1ω   Apply L'Hopital's rule        If limx→af(x)g(x)=0…

Q: 2. The value of lim is (z.v)-(0,0) Vr² + y? (b) 1 a) 0 (c) 2 (d) does not exist

A:

Q: Find the limit 4x2+17x lim x+0 ex-1 a. 1 17 b. None of these. c. с. О O d. 17 е. 1

A:

Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: Find the value of the positive constant c such that....

A: Given- limx→∞x-cx+cx=14 To find- The value of c. Concept Used- If any limit of the function fxgx in…

Q: ow that lim (x,y) → (0,0) 4 3x² + y² 5y does not exist.

A: To show that limit does not exist.

Q: 16x4+9y12 (x,y)→(0,0) 4x²+3y6 Show that lim does not exist.

A:

Q: Evaluate the limit 2x + 4 lim I→ 0 3x2 - 7x + 7

A: Given

Q: V1+3x-1 lim Answer: 1 %3D

A:

Q: Use the e-d definition to show that lim x2 I→2

A: In this question we will use basic of calculus i.e basic of limits. We will simply find the limiting…

Q: Use l’Hospital's Rule to show that lim 1+ X. = e. コ

A:

Q: 10. lim 2-と is A. -1

A: we have to find the value of the given  limit  lim    x→-∞2-x2x

Q: If f(x) = 4" , then lim %3D (A) 4 (B) ! 1.

A: f(x)=4xlimx→0f(x)-f(0)x-0=limx→04x-40x=00, indeterminate form. Apply l'hospital rule to simplify

Q: If p(x)=x²+2x -3 and q(x)=x3-1, then lim 3p(x) 4q(x) x+1 II

A:

Q: Evaluate the given limits: a) 2x3 + 5x² + x – 1 lim x→+0 e2x -

A:

Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: Use the –δ definition to prove that lim x→1 (3x + 5)/2 = 4.

A:

Q: Find lim 4(x) (x) / X-0 x 2. Prove that B(m, n)

A: Limit of the bessel function

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.

Q: Evaluate the limit: 7t3 – 4t = lim t→ 2 %3D

A:

Q: 7xy? Find lim if it exists. (x,y)→(0,0) x² + y2°

A: