lim X → -00 .2 x - x

Q: If the fucntion f is undefined at x then lim f(x) does not exist. = c, C, FALSE O TRUE

A: Given- If the function fis undefined at x=c then limx→cfx does not exist. To Check- If the above…

Q: 4. Evaluate the following limits (3+1)2-9 x2 (b) lim,1 (a) lim,0 x-1 x 1

A:

Q: Find the limits limx→0+{1 + 1/x}x

A:

Q: If x3 f(x) s x for x in [-1,1], find lim f(x) if it exists. X-0

A:

Q: 2. Select the best answer below: lim (2x-13 X (-1)* O -2 O does not exist

A: We have to find the limit and select correct option

Q: 2. Construct a table of values to investigate 1 if x -1

A:

Q: then

A: The given statement is False.   The detailed solution is as follows below:

Q: Find the limits lim tan x x→(7/2)

A: The limit of a function fx at x=a is given by: limx→a fx=fa Also, the left hand limit of a function…

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: show that : Lim h→0  h / √5h + 4 − 2 =4/5

A:

Q: 3. Evaluate this limit. x + 4 lim x--4 4x + 16

A: given,

Q: Evalate the limit 6. lim (e + x)²/x

A:

Q: If (x, y)lim(2, 3) f(x, y) = 4, can you conclude anything about f(2, 3)? Explain.

A: Assume the function z = f(x,y).First observe the value of the limit for x followed by y.

Q: Use continuity to evaluate the limit. 32 + Vx lim x→4 32 + X

A:

Q: 4. lim ) ズ→1 Xー1

A:

Q: Show that lim,→»(1+ e* for any x > 0.

A: To prove:

Q: to if iz fx) < x (x)_ +4x+4,for allx, find Lim f(x)

A:

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: Prove that lim x approaches c  .......... ƒ(x) = L if and only if lim hS0 ƒ(h + c) = L.

A: We have to prove that if limh→0fh+c=L then limx→cfx=L. First, consider limh→0fh+c=L and solve the…

Q: Find the limit. lim (2 – x)7 tan(=) x→1

A: It is asked to evaluate the given limit. For solving the problem we need to know some basic…

Q: 10sin (Tx) In (xº) q(x) What is lim g(x)?

A: solution :

Q: Which property of f(x) = x' allows us to conclude that lim x = 8? x+2

A: f(x) =x3

Q: 4. Use the e, 8 definition to show that lim,- (4x + 5) = 9.

A:

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

A:

Q: if f(5) = 4, f'(5) = 7, then lim of (f(x²+1) -4)/(x²-4) = ?? when x goes to 2

A: Please see the answer below.

Q: 4-If. 2-x < f(x) < 2Cos(x) for all x then find: lim f(x)

A: I applied sandwich theorem which is defined as

Q: 3. Show that if x > 0 for all n e N, then lim(x,) = 0 if and only if lim(1/x,) = +oo.

A: Consider the given information. xn&gt;0 and limxn=0 Now, use the limit definition of the sequence.…

Q: If 1/(x^2 + 1) ≤ f(x) ≤ 1 + x^2 for all x in the interval (−1, 1), what is lim x→0 f(x)?

A: Please refer the attached image for complete solution.

Q: If 5-4x sf(x)s5-x for - 1<xs1, find lim f(x), lim f(x)%= f(x) =D

A:

Q: 2. Use Squeeze Theorem to find lim,x f(z), if for all z >4 6e - 15 < {(x) < VI- 2 2e

A:

Q: Find the limit. lim (2 – x)3 tan(a) x→1

A: limit

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: Show that 2 x² - y² - 1 lim (x,y) →(1,0) 1 − x + (2y)² - does not exist.

A:

Q: 6. Use the e, 8 definition to show that lim,2 x + 1 x+ 3 emlin

A:

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

A: To show that limit does not exist.

Q: The limit lim (x,y)→(4,-5) exists and equals to Select one: O True O False 25x²-16y² -5x-4y -40

A: Given the limit is  limx, y→4,-5 25x2-16y2-5x-4y.

Q: Determine the infinite limit. lim 3 sec(x) x- (T/2)+ X 00 - 00

A: Given limx→π2+3xsecx, to find the limit

Q: show that lim(x,y)→(0,0) (x^3+xy^3/x^4+y^2) does not exist.

A: We will see that along y=mx2 path limit does not exist which means limit does not exist.

Q: Evaluate the limit. lim X→∞ 5 (₁ + 2/2 + 1/2)² X

A:

Q: (2) Suppose that a function f(x) is defined for all real values x except x* x,, then lim f(x) does…

A: For limit to be exist at a point, left hand side and right hand side values of function should be…

Q: 5- x2 37. lim In 1 + x

A:

Q: 3. Show algebraically that lim x* – 2 – x = 0

A:

Q: If + 1for all positive x-values, then what is lim f(x)? X- 4

A: We have to find limit

Q: Use continuity to evaluate the limit. 8 + Vx lim 8 + x

A: We have to evaluate limx→18+x8+x Important formula  If fx is continuous function then limx→afx=fa

Q: 2) If 2 – x2 < f (x) < 2+ 3x² whenever -1 < x < 1, use limit theorems to find lim0 f (x). Give all…

A:

Q: Prove that lim x-y does not exist. (x.y)(0.0) x + y

A: lim(x,y)-(0,0) (x-y)/(x+y) does not exist.

Q: prove that lim x-2 f(x)=4 if f(x)= x^2, x does not =2…

A: Given,           To prove limx→2f(x) = 4 and f(x) =x2      if  x≠21        if x =2

Q: ƒ (₂) If lim fx x-0 = L then which of the following must be true?

A: