b) The function g is defined by 4 x<-2 2-x (2 – x - 2 g (x) = x = -2 |1- Vx² – 3 x>-2 x+2 Show that lim g(x)exist. x -2

Q: 4 if x 2 Find the value of c such that lim f(x) exists. x→2

A: Given the piecewise function :

Q: 1. Let f(x) = 3² – 2x + 1. Compute lim (x)f – (4 + x)f 0+-4

A:

Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: _15. What is lim f(x)? X-4 A. 0 В.1 С.2 D. Does Not Exist

A: Given: Following graph is given. To Find: 15. limx→4fx=?

Q: (5х-4, E If f(x) = 0<x <1 show that lim f(x) exists. %3D 4x - 3x, 1<x<2

A:

Q: 1- Evaluate the limit a-Lim(x/(x-1) – 1/ Inx) b- lim [In(cos(x))]* c- 2-VX²+4 /sin'x x->1+ x >0 x>0…

A:

Q: Let f(x) = 3x – 4 and g(x) = 8x² + 2x – 2. What is f(x) limx→-1 g(x) O a. -- Оа. O b. 7 4 1 Ос. 8

A:

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim f (x)= 21 b) lim x-x+1=-5 x3 c) limx =8 x→2

A:

Q: Use the Squeeze Theorem to show that lim (x2 cos 12rx) = 0. Illustrate by graphing the functions…

A:

Q: Find lim,-1 f(x) -3 -2 -1 2 O lim,→-1 f(x) = 2 O lim,-1 f(x) = 1 O lim,-1f(x) = -1 Lx→-1 f(x) = –1 O…

A:

Q: 4-Find the limits of the following x -1 1. lim Vx +3 - 2 Vx² +2 2. lim X+0 3x –6

A:

Q: Let f(x) = 3x + 2. Use the € – d definition to prove that lim 3x +2 1. x→1 Definition. E-d proof.

A:

Q: 04: - Evaluate the limit of the following: x3–1 lim x→1 4x3-x-3 sin 2x lim 2) x-0 2x²+x 1-V 3) lim…

A: Q.4). (1) To evaluate the limit: limx→1x3-14x3-x-3. Solution: We can find that it is 00 form. So, we…

Q: 1- Find the limits: VI- lim X X-1 а. 2x3 b. lim x→ 00 3(x-2)2 2x3 с. lim x2 3(x-2)² x+1 d. lim X-3…

A: Given: )

Q: 3. Evaluate the limit of lim(x² + x + Vx + 1) x→3

A: A limit of a function f(x) is defined as a value, where the function reaches as the limit reaches…

Q: 1- Evaluate the limit a-Limx²-4/(x²-x-2) X-2 b- lim [In(cos(x))]* c-2-(X²+4) ¹/2²/sin²x x-0 x →0

A: L'Hospital rule:- If a function is of the form p(x)q(x)   then if limx→a p(x)q(x)  is of 00 or ∞∞…

Q: Show that if lim f(x) = lim h(x) = 3, and if f(x) ≤ g(x) ≤h(x) for 2-0 x-0 all z € (-1,1), then lim…

A: Given that limx→0fx=limx→0hx=3 and fx≤gx≤hx for all x∈−1,1. We have to prove that limx→0gx=3.…

Q: 1 Let f(x) = 1, 0sx<2 -x2 + 4x- 3, x22 . Compute lim f(x).

A: Topic -limits

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: Given a function f:R → R with f(x) = x - 1, for x rational and f(x) = 5 - x, for x irrational Prove…

A:

Q: When the function f(x) satisfies f(1) =1,f'(1)= 3 obtain a value of lim/ (2)" -1 x→1 x² – 1

A:

Q: b) The function g is defined by 4 x-2 x+2 Show that lim g(x) exist. X -2

A:

Q: 11. Determine the limits. In(x) a. lim X→1 X-1

A:

Q: 1. Evaluate a) lim b) lim X-T K1O the limit sinx x²-x2 4 In (1-x) + x + == x² 2 23

A:

Q: 1 Let f(x) =. 1,0sx<2 .Determine lim f(x) -x² + 4x – 3, x 22 X2+

A:

Q: 2. Let f be defined by the equation f(x) = V3-x. a. Evaluate lim f(x) %3D x-3+

A:

Q: Suppose that f(x) = 2cos (n/3 x) and the graph of g(x) is given by: y = g(x) 2 1 -5 -4 i ż 3 4 5 x…

A:

Q: 1) a) Evaluate the limit. 1 1 lim 3 x x+3 x-3

A: Introduction: The limit of a function is the base of differential calculus. When the independent…

Q: 2. Suppose f is a positive function. If lim,»a f(x) = 0 and lim, a g(x) = 0, show that lim [f(x)]•w…

A: limx→afx=0  &amp;  limx→agx=∞

Q: 1- Find the limits: Vx- 1 lim xI x-1 а. 2x3 b. lim X- o 3(x-2)2 2x3 c. lim X-2 3(x-2)2 x+1 d. lim…

A: Given: a)  limx→1x−1x−1=?b)  limx→∞2x33(x−2)2=?c)  limx→22x33(x−2)2=?d)  limx→3x+1(3−x)2=?

Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

A:

Q: 1.) Determine the limit: a) lim vx2 + 14x + 49 x-5 b) lim (x² – 4x)³ x-1

A: Solution:To solve 1a and b1.(a)limx→5x2+14x+49(b)limx→1x2-4x3

Q: 1. Sketch a graph of a function f(x) with the following properties: f(-2) = 0, ƒ(2) = 0, lim_f(x) =…

A:

Q: x2 - 16 - if x>0 x + 4 2) Let f(x) = %3D x2 - 16 - if x<0 X- 4 Find lim f(x). x-0-

A: First I have written the definition of left hand limit , just use this definition for given function…

Q: Use the Squeeze Theorem to show that lim (x² cos 21xx) = 0. Illustrate by graphing the functions…

A:

Q: Determine the value for c so that lim f(x) exists. x-3 f(x) = 5**, *+c, for x 3

A:

Q: b) The function g is defined by 4 x-2 x+2 Show that lim g(x) exist.

A: We will calculate RHL and LHL, to show its existence.

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = 3**c, for x3 %3D

A: NOTE: Refresh your page if you can't see any equations. . find the left side limit of the function…

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: Determine the value for c so that lim f(x) exists. X→3 1 f(x) = 3*+c, for x3

A: Given that,

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: 1. (a) Find the interval in which conditions of Rolle's theorem are satisfied for the function f(x)…

A:

Q: 13. lim )- (2- x→2 4-x Vx+7-J7 14. lim x→2

A: (13) We have the given limit problem as, limx→22-x4-x On calculating the factors of numerator and…

Q: 1.1. Find the limit or show that it does not exist. (a) lim (e + 2 cos 3x) (b) lim vx + ax - x2 + Bx…

A: Note:- In given problem, first problem already has two sub-parts. So, according to guidelines, we…

Q: Find lim f(x). x2 - 16 if x>0 x+4 Let f(x) = x2 - 16 if x<0 X-4 O A. 4 О В. О Ос. -4 O D. Does not…

A:

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: The value of the constant k such that x2-kx+7 lim exits is x-1 x+1 -7 7 -8 8 -6

A:

Q: Prove rigorously that lim (x2 – x) = 6. x→3

A: We have to prove  limx→3x2-x=6 Now let  L=limx→3x2-x

Q: Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). Find limx→3 h(x) algebraically

A: h(x) = x2 - 2x -3x2-4x+3 To find :limx→3h(x) limx→3h(x)  =  9 -6-39-12+3     (By direct…

Q: x² – x + 1 1 - (c) lim x→1 x + 1 2 using definition of the functional limit

A: We can prove the statement as below using definition of limit

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.