2.x2 + x – 2 7. Compute lim Justify your answer A number is not 7x2 – 3x +1 enough.

Q: 1. Compute lim. ( ). 1 x→2+ 2 x² – 2x. where c is a real number. You may need to discuss according…

A: limx→2+1x−2−cx2−2x

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: Prove rigorously that lim (4 + 8x) = -4. X-1

A:

Q: If 3x - 4 s f(x) sx2 - 3x + 5 for x 2 0, find lim f(x). x-3

A: Given, 3x-4 ≤ fx ≤ x2-3x+5              for  x ≥ 0 We have to find limx→3fx

Q: Find the limits in Exercise

A: To evaluate: limx→5-3x2x+10 Solution: limx→5-3x2x+10 On simplifying further we get:…

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

A:

Q: Compute the limit below. Justify your answer. 2x2+5x -52 lim- .3 x-4 X°+9x-100

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: 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: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: Evaluate the limit 7(y² – 1) - lim 3y²(y – 1)3 y→2

A:

Q: Show that |x2-4|<e ,  when 0<|x-2|<e(5+e)-1 and prove limx->2 x2=4 by using these…

A: Note: The statement is verified by the ϵ-δ statement of limit.

Q: 2) a) If a >1, compute lim a* . b) Which grows faster as x → 0, y=2" or y=x² ? Explain your…

A: Since you have posted a multiple questions. So,  we will solve only first question  for you. To get…

Q: Show that 2n lim n+2 = 2,

A:

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

A:

Q: 4. Find the following limits: (a) (b) 2 lim-3 x-3 - 2 4 3-x 12x - 4x² lim x3+x² - 6x +9 1

A:

Q: Lim. 341 そ→+ 6. Find:, 2. -im

A:

Q: Prove that lim x 2 = 4. x→ 2

A:

Q: 2. Evaluate the following limits. x2-4x+4 a. lim x→5 x*-8x³+24x²–36x+16

A:

Q: Prove rigorously that lim (4 + 8x) = −4. x→−1

A:

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

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 limits 2.1 2x + 3 lim Xo Sx + 7

A: To evaluate the limit: limx→∞2x+35x+7 Solution: limx→∞2x+35x+7 On simplifying further we get:…

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

A:

Q: Evaluate the following limits. х* + 3х + 2 lim, 'x-1 v2 x² + 4x +3 a. x² – 2x lim, „2' Vx² +5- 3 b.

A:

Q: Describe the left end-behavior of f (æ) = ²²+ 4z lim z+ 4z+ 1 00 lim 2+4z+1 = 00 I-00 lim 2+ 4z+1…

A: Given :             fx=x2+4x+1x

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: 1. Evaluate the following limits. 3x + 10 – 4 (a) lim 2--2- r2 – 4x + 4

A:

Q: Evaluate the following limits: 3x-14x-5 lim- .2 4.x 5| a) x+5 2x2 -13x +15

A: Find the limit

Q: Use the e-8 definition to show that lim VI = 2. Z-14

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: Calculate the limit algebraically. 7x2+7x-6 lim 10x-2 1. 11 9. 10 10 1/2

A:

Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(4x 2 + 2x + 5) = 5x➔0

A:

Q: 2.) Evaluate the one-side d limitss lim Jx+7 = メラー7 lim xキ7 - メーマー7+

A:

Q: Compute the following limits exactly. 5* -7x +11 (a) lim x3+3x-4 X2 X TIX (b) lim 13sin(-A)-/24x +17…

A: Consider the limits a)limx→25x−7x+11x3+3x−4b)limx→613sinπx4−24x+17

Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: 1. Find the limit of the following: ** - 11х* +37х* +6х' - 297х +621x - 405 x* - 11x* +47х* -114х* +…

A:

Q: Evaluate the following limits: z² + 4z – 12 z² – 2x 3. lim

A: 3) To evaluate the limit: limx→2x2+4x-12x2-2x

Q: x²-4x-5 B. lim ズ→5 ズー5

A: first of all factor the numerator, then apply the limits

Q: Evaluate using the Squeeze Theorem.

A: Squeeze theorem: We assume that our original function is hx, and that it’s squeezed between two…

Q: Show that 13x - 12 can be made as small as desired by taking x close to 4. lim(5x + 2) = 17x➔3

A:

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

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

Q: Given that f(x)={kx2+2,≤22kx,x>2. If limx→2f(x) exist, then k equals.

A:

Q: Suppose that following is true. (x2 + 5 f(x) = {x (6x² - 5 if x s0 if 0 < x < 1 if x 21 What is lim…

A: To check the existence of function at x = 1 We will calculate LHL and RHL if they are equal them…

Q: Evaluate the limit: 7t3 – 4t = lim t→ 2 %3D

A:

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

A:

Q: lim ( 7x 12 6. lim 13B

A: In this question we can find limit . Firstly solve quadratic equation of the numerator and cancel…