2.x+1, xs2 x², x>2 . Find lim f(x) for f(x)= O 5 O4 O 5 or 4 Does not exist

Q: II. Prove that for each of the following lim (x,y)→(0,0) f(x, y) does not exist. ,2,,2 4. f(x,y) x4…

A: limx, y→0, 0x2y2x4+y4

Q: Suppose that f(x, 0) = 3 for all x ≠ 0 and f(0, y) = 5 for all y ≠ 0. What can you conclude about…

A: The limit of the function, f(x,y) at a point (a,b) does not exist if two paths upon which the…

Q: 9. Evaluate the limit. lim (1+ sin 3x)1/x x→0+

A:

Q: b* – 1 Show numerically that for b = 3 and b = 5, lim аppears to equal In 3 and In 5, respectively.

A: Given : limx→0bx−1x

Q: In evaluating S₂²² 2 dx 2 XV x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at given x.

Q: In (x +h) – In (x) is When x = 2e, lim h→0 h

A: Substitute x=  2e above

Q: Solve for the limit: lim \belowx → 3 x2-9 O a. 1. 54 c. 6. 1 54 O d. 1/9

A:

Q: Suppose the inequality (x² – 4x + 3) < f (x) < cos ( TX *) holds for all values of x. 2 Find lim f(…

A:

Q: What is (ro s)(x), if r(x) = V2x – 4 and s(x) = x + 2x? O a. V2x- + 4x – 4 | O b. V2x2 + 4x - 4 O…

A:

Q: Find the limit. lim X-2 x+2 O 1/2 -00 O Does not exist

A: Answer is limit does not exist

Q: Find the value of the limit: 3x -9x e -e lim In(1+x)

A: Using limit to find the value of given function

Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: Find the limits limx→q(ln x)1/x

A: Given,     limx→qln x1x

Q: Find the limit. lim x-2/In x X x-0+ O -2 O e?

A:

Q: I. Evaluate the following limits. 1 1 1. lim x→1+ x – 1 er – e - -

A:

Q: 5. Evaluate the limit: Vx +1 lim x→1 4x -4

A: Limit at a point exists if left-handed and right-handed limits exist and they are equal. Left-handed…

Q: Find (if exists). lim (х,у) — (0,0) (4 + (x² + y²) In(x² + y²; Dose not exist O 4 0 1 0

A:

Q: 1. Show that for all f e L'(R) lim %3D

A: Put the delta = 1 in integral function

Q: 4-IS. 2-x s Mx) s 2Cos(x) for all x then find: lim f(x)

A: It is an application of sandwich principle of limit

Q: Answer the question. 5, x<-1 x = -1 3-x, x2 +1, Wx-2+5, x2 2 2, Given f(x) = %3D -1< xs1 X 1<x<2…

A: Given function f(x)=1x+5, x&lt;-12, x=-13-x, -1&lt;x≤1x2+1, 1&lt;x&lt;2x-2+5, x≥2

Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

Q: 2) If x3 s f(x) sx for x in [-1,1), find lim f(x) if it exists. x-0 A) 0 B) Does not exist C) -1 D)…

A:

Q: Verify numerically that:

A: To verify: limh→0eh-1h=1

Q: 2 Show that the following limit does not exist. lim Ty Cos y (r.9)-(0.0) 3r+ y²

A:

Q: 14. Evaluate the following limits. (3-x+x2, 5x+1Y e) lim 2x y-0+ 5x-7 lim 2 f) X0o ( 3x2 x sin x lim…

A:

Q: Evaluate teh following fucntions

A: Dear Students,  “Since you have asked multiple questions in a single request, we will be answering…

Q: 18. Find (if exists) * lim (x,y)→(0,0) (4 + (x² + y² ) In(x² + y² )) O 1 O Dose not exist - O 4

A: Limit of the two variables function : Let f be a function of two variables .The limit of f(x,y)…

Q: 1. Solve the following limits. (a) lim T→-∞ V1 + x² x In x (b) lim x UJ + x 00x 2+ sec (3x) (c) lim…

A:

Q: 2. Find the limit of the following function sin(x - 4) lim- x-0 x- 2

A:

Q: 2. Find the following limits algebraically. Then support your conclusion numerically. x² – 3x – 10…

A:

Q: 2. The limit of the following function equals: x2/3 + x-1 lim x--00 x2/3 + cos2 x

A:

Q: Estimate the limit numerically. x² lim x+4 O diverges to +o 00 O diverges to -∞

A: Given

Q: 11. Show that the limit lim (z.y)→(0,0) r² + y4 does not exists.

A:

Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

A:

Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

Q: 7 x? 4x + 10 if -1 2 if a < -1 | If f (x) = I-1 | - exists. Enter DNE if the limit does not exist.

A: Here we have to find      limx--&gt;-1 f(x) .

Q: 2. Use Squeeze Theorem to find lim, x f(z), if for all z > 4 Ge² – 15 < {r) f(x) < VE-2 2e

A:

Q: Suppose that functions g(t) and h(t) are defined for all values of t and g(0) = h(0) = 0. Can…

A: Given that functions g(t) and h(t) are defined for all values of t and g (0) = h (0) = 0.

Q: If 2 - x2 &lt;=g(x)&lt;= 2 cos x for all x, find lim x--&gt;0 g(x).

A:

Q: 4. Evaluate the following limits: sin x (a) lim x-0 x³-7x2+10x (b) lim x→2 x2+x-6 sin at (c) lim…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 3. Compute the limit algebraically Vx +3x2 lim 6x 1

A:

Q: 12 Show that the following limits do not exist. 1 lim X0x (a) (x > 0), 4,

A:

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

A: Limit of the bessel function

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

A:

Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

A:

Q: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x

Q: 5x2 + 10х + 1 :0. lim x4 + x? + 1

A:

Q: 3x – 1, if x 8 | Let f(x) = { 5 x+9 Show that f(x) has a jump discontinuity at x = 8 by calculating…

A:

Q: In (x + h) – In x (c) lim h→0

A: To find the limits  Here variable is h , so assume x as constant. 0/0 form , so use L-Hospital's…