3 - x, x < 2 x = 2 2, - Let f(x) = x > 2. y=3-x -2 a. Find lim,2- f(x), lim, 2- f(x), and f(2). b. Does lim,2 f(x) exist? If so, what is it? If not, why not? c. Find lim,-r f(x) and lim,- f(x). d. Does lim,-1 f(x) exist? If so, what is it? If not, why not?

Q: Give precise definitions of the following statements.

A:

Q: ,- 3y sin (4x) - 3y - 2 e sin (4x) Find lim - 4x (х,у)—> (0,0) - 2 e sin (4x) lim - 4x (х,у) — (0,0)…

A:

Q: 2-Given that: lim,-o ƒ (x) = 2 lim,--o g(x) = –-1.2 lim,-o k(x) = 0.8 Find: A- lim,-o[f(x) + g(x) –…

A: Given limx→0fx=2limx→0gx=-1.2limx→0kx=0.8

Q: 1- V1– x2 с) lim x→0 [without using l'Hospital Rule] x2 -1- x – a? d lim x→0

A:

Q: Find the limit (if it exist)

A: Given:

Q: if z 3 f(x) = {3 -1 (a) lim,40+ f(x) (d) lim,-3- f(x) (b) lim,40- f(x) (e) lim,43+ f(x) (c) limz-0…

A: Given the function f(x) = -xif  x&lt;03-xif  0≤x&lt;3(x-3)2if  x&gt;3

Q: 3-Vx+3 6. (10) Find lim analytically (if it exists). X→6 X-6

A:

Q: Find the limit. lim 9. (x, y) 9) x+y-9 VX + y -3 X + y29 0. 3. No limit

A:

Q: ev2x-y lim (x,y)→(3,2) x*-4x2 lim (x,y)¬(0,0) \x²+2y²,

A:

Q: Along the path z= e find 2. lim (2,4)→(1,0) y-4zy 3x-y-3

A: Here, we have to reduce this limit to a limit in a single variable by using the equation of curve.…

Q: 2) IF f(x) = {" (x + 2 , – 1<x<0 x, 0<x< 1 find limf(x) %3D

A: To find lim(x tends to inf) f(x)

Q: f(x) = x²+13z+40 x+5 %3D f(x) f(x) -5.1 -4.9 -5.01 -4.99 -5.001 -4.999 Based on the above, what do…

A: Given ,limx→5x2+13x+40x+5

Q: 0, Let f(x) sin, x> 0. y [o, y sin, x>0 -1 a. Does lim,-0+ f(x) exist? If so, what is it? If not,…

A: a) x-&gt; 0+ means on the right side of x=0 On the right side of x=0, the function is oscillating.…

Q: 3 k3 -ル+} (my)0, t) 4 +n -y lim

A: Given that  Limit

Q: _11. If lim (x² +1) = 2, and x = 2.5, then x->-1 lim (x² + 1) is equal to. x-2.5 A. 5.25 C. 6.25 B.…

A:

Q: f(x)= (x^2-2 where, x/=4). Calculate: lim x-4^- f(x)

A:

Q: - e2 +e-3x 6e4z – e2z +e-3z Given lim 200 7+ e4r – 2e3x = 6, to find lim as discussed in 7+ e4x –…

A:

Q: Vx- 2 4. lim- x-2 x2 - 4 y-1 5. lim- Vy? +3 – 2

A: We can apply the limit to the expression by applying the limit as value for the variable in the…

Q: 3.lf limT(x--1) [(x^3+x^2-ax)] =1-a, then a= O a. 1. O b. 0. C. -1. O d. 1/2. 4-The equation…

A:

Q: (3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge gained in…

A:

Q: x² + 2y? + 3z² 18. lim (x, y, 2) →(0, 0, 0) x² + y² + z?

A: We have to find the limit by two ways method

Q: b) Suppose that limx→md(x) = 10 and lim,-mE(x) = -7 , find lim,-m(d(x) + E(x)) (iii) lim,-¬m(d(x).…

A: Since your question has multiple parts we will solve the first three parts for you. Consider that…

Q: ® Find Lim X->2 x¥ _ 2x² - 8 x² - 4 (2 ,X +2 Lim 3X X→3 X- 3 -3 X+3 O Lim © Lim t- fo -) ,X EO X+2 2

A: "Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: |x– 1, ifz> 0 estimate lim f(x).- [ 1, if z 4 5. а. 1/4 b. 2 c. does not exist d. 16

A: 4. f(x)=1,if x&lt;0x-1,if x≥05. f(x)=1x,if x&lt;4x2,if x≥4

Q: Along the path x = e find lim (2,y)→(1,0) y²+6zy 3x-y-3

A: To evaluate the given limit: lim(x,y)→(1,0)y2+6xy3x-y-3 along the path x=ey. Here,…

Q: ах + 7, х0, find the value of a if lim f(x)exist. xk

A: Topic :- Limit

Q: z² +et= 1-400 2z-e² 2* - 3* 17. lim- x-0 18. lim cotxln(x+1) x-0 16. lim-

A: Note: As per our company guidelines we are supposed to answer the first three sub-parts of the…

Q: y of -4 -2 -2 (a) (1) (b) lim f(x) x-1 2.

A:

Q: x2-x-2 2x-4 2sin(6x–12) 3(x-2) Sx-1 Let f(x)* ,g(x) • and h(x) Vz+2+1 a. Find lim f(x), lim g(x),…

A:

Q: S 1.4x + 0.8, x -2 f(-2) = lim f(x) = x--2- lim f(x) = x--2+ lim f(x) = || x--2

A: E

Q: a) Find two fuctions such that lim, +∞ ƒ (x) = ∞ lim, »0 g(x) = 0 = 00 but lim,->0∞ ƒ (x) – g(x) = 1

A: Consider the function f(x)=x2+1x. Its limit as x tends to infinity will be given by:…

Q: EXAMPLES. Observe that iz +3 lim z→-1 z +1 z +1 =D0 since lim %3D z→-1 iz + 3

A: Now, limz→-1z+1iz+3=-1+1i(1)+3                 =0-1+3                 =0…

Q: 1 d) limy-→0- e) lim,o (1+ r/n)" 1 f) lim→0 x +

A: L'Hospital Rule : If limx→af(x)g(x) is in the form 00 or ∞∞, then limx→af(x)g(x) = limx→af'(x)g'(x)

Q: 3 x 0 and x + 3 3 - x Find lim,--1 f(x) b) lim,o f (x) c) lim,-3f(x) Given that limaf (x) = 2 and…

A:

Q: 5x b) lim lim-0 2ln(x+1) ex-e-x c) lim lim-0 2x x2-2x-3 d) lim lim-3 x-5x+6

A:

Q: 8- 6- y = h(x) y = h(x) -4 -3 2 -2- 2. lim, h(x): 3. lim,→2- h(x): 4. lim,-2+ h(x): 5. limy-2 h(x):…

A: Find the following value from the graph:

Q: -xx2 a) Find lim, + f(x), lim, 2-f(x) and/ (2). b) Dose lim, 2 f(x) exist, if so, what is it? If…

A: We need to find limit.

Q: - [x² + 2 if x < 2 (x) l(x - 3)2 if x 2 2 (a) Find the following limits. (If an answer does not…

A: Given function:

Q: 6. Given f(x)= { 3, if x < -2    x, if -2 ≤ x<8    x+3, if x≥8  estimate lim f(x) x→−2     a.-2…

A:

Q: 2. If lim x, = 1 and lim yn = 0, then it is possible to formally prove that lim(x, – Yn) = 1.

A: (Solving the 2nd question as per our guidelines) Solution of 2: The statement is "If lim xn=1 and…

Q: a) lim,-1- F(x) = b) lim,--1+ F(x) = | %3D c) lim,--1 F(x) =| | d) F(-1) = %3D e) lim,1- F(x) = %3D…

A: We have to find

Q: Let ƒ(x)

A:

Q: f(x+Ax)-f(x), Ff(x) = v2x + 1, what is the lim Дх--0 Ax

A:

Q: Let ƒ(x) =

A: Given, The piecewise function is f(x)=3-x , x&lt;22       , x=2x2     , x&gt;2

Q: 3 - m3 x + 2 2 . lim lim x-2 x + 2'x2 – x – 6 A- m4 lim as x approaches m 1. LO

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 9 – y². |-(16 * 10)x – (4 * 10) lim . -] + lim y--33 + y x + 10 x--10

A: Given,            limy→-39 - y23 + y + limx→-10-16*10x-4*10x + 10

Q: 1. Prove using e-d definition. (d) lim (4x + 3) = 7 x→1 x2 – 9 = 6 - (e) lim x→3 x – 3

A: To prove the limit using epsilon-delta definition

Q: Let ƒ(x)

A: Since you have posted multiple subparts we solve the first three subparts for you to get the…

Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information:

Q: d) If f (2) = 4 then lim [f (x)]² [ Select ] 16 T→2 e) If lim (5f (x)) = 15 , then lim f (x) = 3 . […

A: d) Given: f2=4 But we can not say whether f(x) is continuous at x = 2 or not, if f(x) is continuous…