4. Find the following algebraically. -2x – 4x +4 a. lim x³ – 27 x - 2 b. lim V9x² +1

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

A: Here given

Q: lim V3x² – 6 X-2

A: The given problem is,           limx→23x2-6 Here the function is continuous and defined at x=2, so…

Q: Q1/ Find the following 1. lim + 2 = 3 X00 X 2. lim(5x - 4 + )

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Q. 1. Evaluate the following -x* +3x +5x –18 a) lim 5x – 2x-0.5 Vx² +15 –4 b) lim x-1

A: We have to calculate the limit

Q: Consider the following function T² -7x-18 if x -2 Find lim [f(x)]*. I-2-

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: x* – 2x²y + 4y² c) lim x' + 4y² (xyH0,0)

A:

Q: Q2. Evaluate the following 4-x2 1. lim x-2 3-Vx2+5 t2+3t+2 2. lim t--1 t2-t-2

A: Given: 1. limx→24-x23-x2+52.limt→-1t2+3t+2t2-t-2

Q: Find the following: x+/3 + 9x/5 (2х — 1)4/2 — 3 i. Lim- X-0 6x/2 – 4x'/4 ii. Lim x→5+ х — 5

A: we are solving only part (a) of the question because it contains super subparts. Please upload the…

Q: V10x – 7y – 10 Find lim by rewriting the fraction first. 10x - 7y – 100 (x,y)→(10,0) 10x - 7y + 100

A:

Q: ,3 Find lim (x,y)→(0,0) x² + y² °

A:

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: Write ∞ or -∞ where appropriate.

A: Given  limx→∞1x1/3-1x-14/3

Q: 2. Evaluate the following limits. -7r-8 (a) lim 4x +5 (b) lim 100 3r2-3.r +4 (c) lim

A:

Q: x2 + 8x + 15 if x 2. Find lim f(x). x-2+

A:

Q: Find the following lim (5x – 2) x² – 7x lim 2-3 x + 2 (a) (b) (c) lim(3.r – x") (d) lim I-2 r3 + 4

A:

Q: Evaluate the limits. t2 – 4 lim 42 t3 – 8 | (a) (b) (9 + x)-1 – 9-1 lim 8x2 – 9x + 1 lim a00 3x2 +…

A: limt→2t2-4t3-8

Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

A:

Q: x²+x y-2y lim (x,y)→(4,16) x- Jy

A:

Q: For f(x) = the square root of 7x+30, how can I find f’(x) using the definition f’(x) = lim as h—>0…

A: Given,          The function is fx=7x+30.We know that,          The derivative of the function is fx…

Q: Q1/ Find the following 1. lim x2 + 1 = 2 x00 (x-2)2 2. lim x-2 (x-2)(x+2) 3. lim (5 -) x-0

A:

Q: Ex x-2 XE3, X-2 12) Consider メレ3 2) lim. (f(x) b) lim. (f(x)

A: Topic:- limit

Q: EX- Find Lim -im Z-2Z+4 Z-1-13i

A:

Q: 1. Find the lim zx*-13x-7 by completing the table of values (round off your answers to at most x-7…

A:

Q: If f(x) = 3x2 - 4x +1 and g(x) = x² + 2x - 3, then what is lim 9X, g(x). X-1 f(x)

A:

Q: Find the following: x+/3 + 9x/5 (2х — 1)1/2 — 3 - i. Lim- x-0 6x1/2 – 4x1/4 ii. Lim x→5+ х — 5

A: a)

Q: Suppose p and q are polynomial functions. If lim p(x)/q(x) = 9 and q(0) = 3, find p(0).…

A:

Q: 36. (х, у) —- (0, 0) lim (x + y²) In(x² + y²)

A:

Q: the following limits: x2+x-6 x-4 x2-7x+12 (i) lim

A:

Q: 4. Given that f(x)=4x - 3 f (1+h)- ƒ(1) Find lim ,x21

A: Given query is to find the value of indicated operation.

Q: Suppose that following is true. x2 + 6 if x s 0 if 0 <x < 1 f(x): 7x² - 6 if x 2 1 What is lim f(x),…

A: Just compute right hand limit and left hand limit and see if they are equal or not.

Q: nd the one-sided DNE lim_(x². +x+5) x--5- exists). (If an answer does not exist, enter DNE. Submit…

A: Topic:- limits

Q: 18) Find lim f(x) %3D X 2 - A) – B) 2 00 C) 1 D) 4

A: Topic = Limits 18) B

Q: Q2. Evaluate the following 4-x2 1. lim x→2 3-Vx²+5 t²+3t+2 2. lim t--1 t2-t-2

A:

Q: Using the Sandwich Theorem

A:

Q: Q.2 Show that r(ax) _ 1 lim x0 (x)

A: to show  limx→0ΓaxΓx=1a   ...i as we know Γn=Γn+1n using this formula we get Γx=Γx+1xΓax=Γax+1ax

Q: ラメー 2. for) = X ニ 3メ-1 lim (fog)x メーラ

A:

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

A:

Q: 4. Find the following limits: 3x2 – 7 - b) lim x² + 2 Зе" + 4е 8 d) lim r→0 5e* + 4e-x e) lim I→8- X…

A:

Q: If 8x – 19 < f(x) < x² + 4x – 15 determine lim f(x) x→2 What theorem did you use to arrive at your…

A:

Q: If f(x) = 4" , then lim %3D (A) 4 (B) ! 1.

A: f(x)=4xlimx→0f(x)-f(0)x-0=limx→04x-40x=00, indeterminate form. Apply l'hospital rule to simplify

Q: If p(x)=x²+2x -3 and q(x)=x3-1, then lim 3p(x) 4q(x) x+1 II

A:

Q: g lim y²+6y y¬T [/y+1-3y2 y+1-3y²

A: Using standard limit substitution

Q: Which of the following is your solution to lim Vx² +2 = ? x-0 3x -6 O 1/3 O -3 O -1/3 O 3

A: Given  The limit expression is  limx→∞x2+23x-6 .

Q: 22 - 3x + 2 1 3. Find lim as g3 - 2x2 (a) a→0+ (b) T 2+ (c) 2 (d) 2 (e) What if anything can be said…

A:

Q: Find the following: (i) Lim      x^1/3 + 9x^1/5     x→0    6x^1/2 - 4x^1/4 (ii) Lim…

A: i) Since it is in 0/0 form, so we can apply the L'Hospital's rule

Q: -10 2468 10 x -4+ ad • +8- -10- Find lim f(x) = %3D

A: The graph of the function f(x) is

Q: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 1+2- 12 - 4x + 4

A: