Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain why or give an example that disproves thestatement. If f is continuous at 5 and f(5) =2 and f(4) =3, then limx->2f(4x2 -11) =2

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A: We distribute the limit and simplify

Q: Evaluate in terms of the constant a.

A: Limit for the given expression can be computed with two methods. First is to expand the numerator,…

Q: Letf(x) =(12x+a)/(7−bx). Find the values of a and b, given that limx→∞ f(x) =−2 and f(1) = 17.

A: Use the first condition for f(x) to find b.

Q: If f(a) - (9x 3), then lim f(x) = エ

A:

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A:

Q: Which of the following graphs below show that lim f(x) exists? x-3 34-x i ii iii

A: Limit of a function means the value 'p' function approaches when 'x' approaches 'a'.

Q: find the limit or explain why it does not exist

A:

Q: Find the value of lim f(x), if x→3- S8x2 – 3 |5х + 7 f(æ) = x 3 O 69 57 66 45 22

A:

Q: let fcx)-x2+てメー1X, five a) limf(x) メ -7 O b) lim f(x) Xー70

A:

Q: If V5 – 2x? < f(x) < V5 – x? for -1 <x < 1, find lim,-o f(x).

A: Given  5-2x2 ≤ f(x) ≤ 5-x2 for  -1≤x≤1.

Q: Evaluate the limit, If it exists. (If an answer does not exist, enter DNE.) x2 - 8x lim X-1 x - 7x -…

A:

Q: Given f (x) = -4x² + 2x – 5, find limx→h (x), if possible.

A:

Q: Find the value of lim f(x), if f(x) = 6x + 3 x 4 54 54 O 16 12 30

A: Need to find.limit

Q: Given the function f(x) = 5x2 - 3x + 5, determine: f(z) – f(x) a) lim Z-X b) f(x)

A: Please refer the attached image for complete solution.

Q: Find the value of lim f(x), if x→2+ 7x + 5 x 2 21 11 13 33

A:

Q: Find the one-sided limit (if it exists). (If an answer does not exist, enter DNE.) 9. lim x2 + X→-7-…

A:

Q: A. Complete the table of values to find the following, if they exist. (1 – 5) 2x+1 lim X2 x-3 X f(x)

A:

Q: What is the sign of the coefficient multiplying x' if f is a polynomial of degree 7 such that lim…

A:

Q: Fill in the blank so that the resulting statement is true.

A: We have to fill in the blanks: limx→a x=_____ Since this is determinate form of limit so we need to…

Q: If 2x < g(x) < xª – a? + 2 for all x, evaluate lim g(x).

A: We will use sandwich theorem to find th required result.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) 6 - Vx lim x-36 36x – x2

A:

Q: Given: -2 < x < 0 x = 0 2, x+ 1, f (x) = -x, 0 <x < 2 0, x = 2 х — 4, 2 < x < 4 What is the lim f(x)…

A: We need to find limx→-2+fx Now, finding the limit as x tends to a+ means that that we need to find…

Q: Given: -2 < x < 0 2, x + 1, x = 0 0 < x < 2 0, f(x) = -x, x = 2 2 < x < 4 х — 4, What is the lim…

A: Given:  fx=x+1,-2&lt;x&lt;02,x=0-x,0&lt;x&lt;20,x=2x-4,2&lt;x&lt;4

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A: limx-&gt;5f(x)=0, limx-&gt;5g(x)=0To check:limx-&gt;5f(x)g(x)

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A: Given- limx→1x-3x2+2x-4=limx→1(x-3)limx→1(x2+2x-4) To find- Whether the above statment is either…

Q: Determine if lim f(x) exists. Is the function continuous at x = 2? Show all the steps. f (x) = { 4 S…

A: Given that a function and we check that at x= 2 this function is continous or not . We know that if…

Q: Evaluate the limit or explain why it does not exist t t- 2-0 √4+t-√4-t x³+1 lim X-1 X+1 Ix-21 lim…

A: Given that some limit problem and we solve this given problem by using general property of limit.…

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) Vx2 + 25 13 lim x→-12 x…

A:

Q: Evaluate in terms of the constant a.

A: The limit of a function limx→Xfx=Y means that value of  function fx can be as close to Y by making…

Q: When lim f(x) exists, it always equals f(a). State whether this statement is true or false. Xa

A:

Q: Determine whether the statement is true or false. If g(x) = x5, then lim g(x) – g(2) x → 2 = 80. %3D…

A:

Q: Determine if lim f (x) = f(c). Write YES if limf(x) = f(c), otherwise NO. Show your proof 1. f(x) =…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Let limx-2 f(x)=-3, and limx-2 g(x)=4, Find limx-2 [f(x)/5g(x) +2f(x)g(x)]

A: Topic = Limits

Q: 4. What is the sign of a if f(x)= ax' +x +1 satisfies lim f(x) = 0? x→-0

A: Given that fx=ax3+x+1 satisfies limx→-∞fx=∞. Note that the given polynomial having odd degree.

Q: Use algebra to evaluate the following limits. 3x4 - 5x² x² 2x² - 2x-12 a) lim x-0 b) lim x+3 x²-9

A: Here we will use basic limit laws and algebra to find the limits.

Q: Use the graph to determine whether the statement is true or false. 2) lim f(x) exists. x -> -3 A)…

A:

Q: Use the table to find  limx→9f(x)limx→9f(x) x 8 8.9 8.99 9 9.01 9.1 10 f(x) 10 11.8 11.99 10…

A: Givenlimx→9f(x)

Q: Evaluate the limit, if it exists.

A: Our Aim is to evaluate the limit of the function given below:-limx→-1 2x2+3x+1x2-2x-3-(i)

Q: Determine whether the statement is true or false. If it is true, explainwhy. If it is false, explain…

A:

Q: Find the value of lim f(x), if x→3+ f(x) 6x + 2 x 3 2x + 6 12 8 18 36 11

A:

Q: Find the limit or show that it does not exist. V1+4x6 (1) lim x- 2- (2) lim (V9x2-5x+3x

A: 1. limx→-∞1+4x62-x32. limx→∞9x2-5x+3x

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + 6x + 9 lim X→-3 x4…

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: Plot the function f(x) then evaluate lim,-1- f(x) -x - 2 if r -1

A: We have to draw the graph

Q: find the limit or explain why it does not exist

A: a. Given that limx→0 x2+xx5+2x4+x3. Compute the limit as follows. limx→0 x2+xx5+2x4+x3=00  I.F Apply…

Q: What is the sign of a if f (x) = ax³ +x +1 satisfies lim f(x) = o0? X -00 %3|

A:

Q: ) Evaluate the function  f(x) =x2   -(2x/1000 )for x=1,0.8,0.6,0.4,0.2,0.1 and 0.05 and guess the…

A: Given function, f(x)=x2-2x1000

Q: Find the value of lim f(x), if f(x) = x3+ 6x + 2 x 3

A:

Q: Use the graphs to identify the values of c for which lim f(x) does not exist. (Enter your answers as…

A: Find the value of c

Q: Let F(x) = 2x²-3x ,does lim_F(x) exists? |2x-3| X-1.5

A: Consider the definition of modulus function, x=x; x&gt;0-x; x&lt;0 The function is given as,…

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.