2. Find the composite functions f°g and g°f 3 when f (x) = and g(x) = x² – 1. x+1 Estimate the limit numerically for lim ズー4 X-4x2-3x-4 3.9 3.99 3.999 4 4.001 4.01 4.1 X-4 x2 - 3x-4 And the answer for lim X-4 x-4 x²-3x-4

Q: Determine whether the function x2 + 2 x > 2 f(x) = x = 2 is continuous at the 4х — 2 x < 2 given…

A: First of all we will find the left hand limit at X equal to 2 and then find the right hand limit X…

Q: Q.3 Find the following limits: x+3 3.1 lim→-3 x2+4x+3 x² +4x+3 x+2 3.2 limx-2 Jx² +5-3 u-1 3.3 lim-1…

A: As per the company guidelines we can solve first three parts . I hope that the given solution will…

Q: (1) Determine the domain and range of g(x,y) = /9-x2-y2. For the following, evaluate the limits at…

A: use the definition of limit , for finding the limit.

Q: 1. Consider the function fx3x+2, -x-6, x>0x<0. Use table of values to find the limit of the…

A: The given function,  f(x)=x+2,x&gt;0-x-6,x&lt;0

Q: 1. Find the limit if it exists. V2 + t – /2 – t - lim t→0 3t

A:

Q: Use l'Hôpital's Rule to evaluate the limit. COS X lim -X- 3. 3. O A. -3 V3 O B. C. 2 O D. -/2 1.

A: We have to find limit As per guideline we have to solve one

Q: Guess the value of the limit (if it exists) by evaluating the function at the given numbers. (4 +…

A:

Q: 1. Evaluate the limit for the graph lim f (x). x→1" f(x) 51 4- 3 2 1- -3 -2 -1 1 2 3 4 -1 а. 1 c.…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: For the function f(x) (X^2-3 if -3 ≤x2 C) is f continuous at x=2? D) does lim f(x) exist at x->4^-?…

A:

Q: Evaluate f(-1+h) – f(-1) lim where f(r) = 5z'+1. Enter I for oo, -I for -oo, and DNE if the limit…

A:

Q: 1 Discuss the existence of the limit lim x 0 x2"

A:

Q: Evaluate f(4+h) – f(4) lim h→0 h where f(x) = -5x – 1. If the limit does not exist enter DNE. Limit…

A: We have to find the limit.

Q: 2x+1 if x < 2 Let f(x) = x²-1 if x ≥2 Determine the one-sided limit lim f(x). x 2+

A:

Q: 4-ху Find lim (x,y)¬(2,1) x²+3y2 if it exists, or show that the limit does not exist.

A: limx, y→2, 14-xyx2+3y2Plug in the value x, y=2, 1=4-2· 122+3· 12=27

Q: find the limit of g(x) as x approaches the indicated value.

A: the given expression is: limx→51x+g(x)=2

Q: 10. Determine which of the following limits exist and does not exist. a. b. 2 - 2 3x - 9 lim 25 * +5…

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly…

Q: 9) Find the limit, if it exists, or show that the limit does not exist: lim (x,y)→(0,0) xª + 3y4

A:

Q: (-1)"f" cost =1--+ 4! 2 (2n)! In(1+t) =t-+ 3 -.+(-1)*-"4 +... n Yukarıda verilen cost ve In(1+x)'in…

A:

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 Зx3-9х2 +х-3 1- lim x→0 sin4x 2- lim…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 2. Consider the function: + 3 if x 2 %3D 17 if x = 2. %3D Find lim, 2 f(x).

A: Function given is- f(x)=x2+3       if x&lt;2x3-1      if x&gt;217           if x=2  To find…

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: Determine the limit at infinity x+x-6x first.) x+x2-6x lim (x-x2 -6x) (Hint Multiply by O A. 0 OB. 6…

A: To Determine: Compute the limit

Q: 4. Evaluate the limits of the following functions: a) limsinx x-0 sin x-tan x 6 b) lim x-2 x2+2x-8)…

A:

Q: 2. Calculate the limit algebraically. x-11 lim O -1.8 03 -0.6 O 1.8

A: Given

Q: Find the value of b-2a for which the limit ex – xex – cosbx - limx +0 exists 4 Select one: а. 3 b. 1…

A: L'Hospital's rule is a useful method to find the limits of indeterminate form. There are two…

Q: Evaluate f(4+ h) – f(4) lim h0 where f(x) =5x +7. If the limit does not exist enter DNE. Limit =

A: f(x)=5x+7

Q: Q4)A) Find the following limits (for two only). x+1 1. limy--17-x-2 1-VE 2. limy-1 1-x 2x 3. lim--0…

A:

Q: 4. The graph of a function f(x) is shown at right. If g(x) = V1+ 3x , find lim [f(x) + 3 g(x)]. %3D…

A: The graph of the function fx is given. From that graph it is clear that, the function fx, at x=1…

Q: Consider the following. x² - 2 if x # -1 if x = -1 f(x) = %3D y -2 -1 1 2 Use the graph to find the…

A: The given function is f(x)=x2-2    if x≠-1-3        if x=-1. Graphically: From the graph, it can be…

Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

A:

Q: 2. Compute each limit. 1- x2 (a) lim I40 1 1 (b) lim +1 1- x 1– x² (c) lim 1- r4 (d) lim z+o 1- x 1-…

A: Here we find the limit value.

Q: Find the maximum value of & > 0 that satisfies the limit claim corresponding to e = 0.3, that is,…

A: In the question it is asked to calculate the maximum value of δ for the given function limx→59-x5=8

Q: 1. Complete the table of values to determine the limits of the function. f(x) = = -1-0.5 -0.1 -0.01…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists or the…

A:

Q: 22) Find the limit equation of f'C4) if リメト=(×23 で allim Jx -2 x-4 b) lim X-4 C lim x-4 X-L X-4 a)…

A: Here we will find the limit equation for f'(4),

Q: 1. Investigate the limiting behaviour of x2 lim (x,y)¬(0,0) x2 +3xy +y2

A: It given function fx,y=x2x2+3xy+y2. When x,y=0,0 in fx,y=x2x2+3xy+y2 will result in 00. Set the…

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x-0 sin4x 2- lim…

A:

Q: .t 5-1 lim t t → 0

A: By L' hospital rule we solve above limit.

Q: Q5. Evaluate the limit Vx+h- Vx lim h-0 Vx+h+Vx in the two cases (i) x > 0 and (ii) x = 0.

A: Evaluating:                                    limh→0x+h-xx+h+x   In the cases:…

Q: : A- Find the limit for the following functions: - tan2x 1- lim X-0 sintx 4x-3 2- lim x--0 Vx2+1 3-…

A: L'Hospital's rule states that for functions f and g which are differentiable in an open interval…

Q: 1. Calculate the limit numerically. lim(x + 11) x→2

A:

Q: Find the limit of f(x)

A: Given information

Q: Find the following limits. √x-3 X-9 x-9 1. lim t²-7t+10 2. lim- t-2 t-2 3. A function f(x) satisfies…

A: Since, you have posted multiple questions, as per guidelines, we"ll solve only first three…

Q: 8. Let f(x, y) be the function x3 + y3 xy? Show that the limit lim(9)→(0,0) f (x, y) does not exist…

A:

Q: 2. Complete the table by computing f(x) at the given values of x, accurate to five decimal places.…

A:

Q: Q1: Find the limit of the following х-2 2x2+1 tan nx 1) lim- 2) lim x-0 (2-x)(2+x) 3) lim x-2 x²-4

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Evaluate the limits numerically. x-1 a) lim x-1 vx+3-2 x² +3x+2 b) lim x--1 x2-x-2 cos(x)-1 c)…

A:

Q: Find the limit. lim (e 4/x+ 9x) x/2 x-0 0 1 00 e2

A:

Q: 1.16 Let f(x) = lim_f(x) = H-4 2, 4x + 19, Calculate the following limits. Enter DNE if the limit…

A:

Q: b. For what value of (k) is the function y=f(x) continuous at x-3. x3-3x2-4x+12 x + 3 x-3 f(x) = %3D…

A: