V4 - x2 0sx<2 lim f(x), where f(x) = < 2 9) x-4" 2 sx<4 x = 4 B) Does not exist A) 4 C) 2 D) 0

Q: What is lim x=inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^(3n)] + 2? (express answer as x,y)

A: Solve the following

Q: Use the Squeeze Theorem to evaluate the limit: limx→0  x cos(8/x)=

A: We know that cos always has a value between -1 to 1 So,

Q: et +ex -x²-2 Lim- x-0 sin²x-x²

A:

Q: Use the definition of a limit to show that (i) limx→0 (x^2 + 6x + 9) = 9 (ii) limx→−7 and…

A: Authoring guidelines:…

Q: 2. Find the limits. limx→-1 sin(x² + 3x + 2) x³ + 1 M

A:

Q: Let Sz+8 3x +8 I-1 Approximate lim f(z) numerically and verify your answer graphically. If it does…

A:

Q: x + tan x 2? — 5х — 14 - (а) lim x0 3x + 4x² (b) lim (Do not use L’Hospital rule in part(b)) x7- x2…

A: Using rules of limit's.

Q: 2.y lim (x.y)-(0.0) 12x- Show that does not exist. -1ly

A: We will show that limx, y→0, 02xy212x2-11y4 doesn't exist. One path: (along x=0)    limx, y→0,…

Q: Q3 :(A): By using "L' Hopital rules"; Find the limits of : 1 (1) lim,-ol1-cos x sin2x (2) lim,…

A: 3)1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0(tan-1x-x) /x3 Repost the next question.

Q: 2. Explain why f(x, y) must approach a unique number L as (x, y) approaches (a, b) along all paths…

A: A number L is said to be the limit of a function f(x,y) as (x,y)→a,b , if for any real number ∈&gt;0…

Q: What is lim x-inf (x_n) and y=lim sup (x_n) where x_n = [(-1)^{3n}] + 2? (express answer as x,y)

A:

Q: Use L 'Hopital's Rule to find the limit:

A:

Q: 2) Show that sinax _a lim x-0 tanbx b %3D

A: Show that  limx→0sinaxtanbx

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol 1-cos x sin²x (2) lim, o…

A: 3 1) limx-0[1/(1-cosx) -2/sin2x ] 2) limx-0 (tan-1x-x) x-3

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

A:

Q: Evaluate the limit. –1+}² 1.2 COS I lim 2.x4

A:

Q: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

A:

Q: 8. Using squeeze theorem, show that the following limit (x – 1)² In x = 0. lim (x,9)→(1,0) (x – 1)²…

A:

Q: The value of limit x→0 of {sin (a + x) – sin (a – x)}/x is

A: we have to find the value of  limx→0sin(a+x)-sin(a-x)x

Q: B) Find the limits by using L.Hopital rule : x²–16 2. lim x→4 (Vx+5)-3

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Does lim (x,y)→(0,0) x² + y² y2 exist? Explain.

A: Here given  limx, y→0,0y2x2+y2

Q: is lim x = inf (xn) as x, y. What Express answer and = 3n lim sup (xn) where Xn = [(-1)³ ]+2?

A:

Q: & Prove that lim I = 2 using the e-d-definition. Hint: Vr %3D

A: Given: To explain the given statement as follows, Here, prove that limx→4 x = 2.

Q: 4 – V* lim x 0 2 + Vx

A:

Q: lim (x,y)-(-3,4) (x³ +3x²y² - 5y³ +1)

A: Here we have given an expression with limit and we have to solve it. We have lim (x,y)→(-3,4) (x3 +…

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim x-0 sin 2x x2-16 2. lim x-4 (Vx+5)-3

A:

Q: II. Evaluate the limits. tan 0 2. lim 0 -0 sin 20 (y-#)* 2. 4. lim t 1-sin y y - 2 2.

A:

Q: Find the limits in Exercise

A: Given: limθ→π4tanθ-1θ-π4

Q: Consider the function f(x, y) 2y (a) lim (x,y)→(0,0) f (x, y) does not exist by using different…

A:

Q: The limit lim (n+1-vn- (A) equals-x (B) equals 1 (C) equals ( (D) equals +∞ O(E) does not exist

A:

Q: 1 Lim x→0* x0x 1 sin x

A:

Q: Q3. Compute the following limits if they exist. SEC x – 1 (а) lim x→0- sin x (b) lim x→0 x tan x 2 -…

A:

Q: lim (x,y)→(0,0) x3y is equal to----- x6+ y2 (a)1 (c)does not exist (d)-2

A: In the above problem, at the point (0,0) the function is not continuous. So, it is not possible to…

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim X0 sin 2x x2-16 2. lim X+4 (VI+5)-3

A: *to find :- limits, using L-Hopital rule.

Q: 3. Use Squeeze Theorem to evaluate lim 1-0+ sin(In r) In(sin æ)"

A:

Q: B) Find the limits by using L.Hopital rule: 7x 1. lim- X0 sin 2x -16 2. lim X-4 (Vx+5)-3

A:

Q: Find the limit sin 2z cot 8z lim z→0 z cot 4z 16 2 does not exist 4 3/2 O 1 O

A:

Q: 2. Find the limit using Squeeze theorem 1 lim-2|x – 2| sin( r - 2

A: Squeeze Theorem- Let f, g and h be functions defined on an interval I. Let c∈I be its limit point.…

Q: 2. Show that lim (x,y)→(−1,0) (x + 1)² sin y (x + 1)4 + y² does not exist.

A:

Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: lim, S(x), given 7-4x. x < 1 S(x) = { %3D x² + 2 x 21

A: Given: fx=7-4x,  x&lt;1x2+2,  x≥1

Q: Show that lim (x,y) → (0,0) 12 √16x +9y¹ 4x²+3y does not exist. Please show a complete solution.

A:

Q: Find the limit. lim (2 – x) tan(3«) %3D x>1

A:

Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

A: Limits using L'Hospital Rule

Q: lim (x.y)>(0,0) 2x sin y 2x +y Use the &- d definition of the limit to prove that

A:

Q: (i) Prove that Lim Vent +1 1 1 + + + /2n²+n] ... V2n2+2

A: Given that, g(x)=limn→∞12n2+1+12n2+2+....+12n2+n from sandwich theoram we can say if f(x)≤g(x)≤h(x),…

Q: x-3- – 3VA lim x+0* 0" x- Vx

A: We first try to find the limit  by substitution

Q: If f(x) = xcosx then limf(x+h)-f(x) h COSX = ? %3D %3D h-0

A:

Q: lim aVx + 3 – b = 1, x - 1 Score А. 4 E. 1 В. 2 С. 1 4 -IN-IA

A: We can make it easier for you.