1. a. Evaluate the following limit: 2x3-128. lim( Vx-2 3x²+kx+k+3Y b. Find the number k such that lim exists, then find the limit x2+x-2 x--2

Q: Prove, using the e-d definition of limit, that: (a) lim x² + 1 = 2 24-1

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: Evaluate the limit, if it exists. ( 6. lim t-0\ 을) tV1+t

A: We have to evaluate the limit: limt→09t1+t-9t Since it is ∞-∞ so simplifying  the limit, Taking 9…

Q: Find the limits x² - 7x lim X-o X + 1

A: Given: limx→∞x2-7xx+1

Q: 1. Use the properties of limits to evaluate the limit if it exists. 3x2+ 7x – 2 lim x→1 3x2 – 4x – 2…

A:

Q: We are asked to estimate the value of the following limit. lim (2 + h)4 - 16 h-0

A: Consider the given table: As h is approaching 0, f(h) is approaching 32.

Q: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x2 + 25 – 13 lim x--12 x…

A:

Q: 11. Show, via illustration, that the limits lim x and lim a are equal but the functions in each…

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: Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.) x² - 6x + 4 lim X→ 2 X-2

A:

Q: 3. lim (4x+1) wt x

A: Given that;  Lim x-0+  (4x+1)^cotx

Q: d) Evaluate the limit lim msec(x). x5

A: In the given  question  msec denotes the slope of the secant line joining the points (5, f(5))…

Q: 1 lim ty1 + t

A:

Q: Find the limit, if it exists.

A: x→-∞lim2x(x6-1)13This is ≡∞∞ form so L'Hospital rule will be applied.

Q: 4-Find the limits of the following; r-1 1.lim x+3-2

A: Answer

Q: Determine the limit algebraically, if it exists x3 + 12x2 – 5x lim 5x O -1 O 5 DNE

A:

Q: (4) Evaluate the limit, if it exists. 9 – x lim 1→-00 3.x³ – 75

A:

Q: Find the limit, if it exists. 5x2 lim +14x – 3 x→-3 2x +6 1 2 O 5 2 O -8

A:

Q: Evaluate the limit, if it exists.

A: limh->09+h-3h

Q: Find the limit, if it exists.

A: Given: L=limx→-∞5x2x+3 For evaluating given limit, we simplify given expression and evaluate the…

Q: 2. Determine the following limit. 450 lim x→∞ 9+3 .1.2-0.25x+10

A:

Q: Evaluate the limit, if it exists. lim –x3 h (x + h)³ h-0

A:

Q: Evaluate the limit, if it exists. (If an answer does not exist, erter DNE.) V 25 + h - 5 lim h - 0

A:

Q: Use the e - 8 definition of the limit to establish a ô that proves lim (x – 1) = 2 x-2 O A) 3 B) 2e…

A:

Q: Find the following limit or state that it does not exist. x²- 5x +4 lim X-1 X→1

A:

Q: Evaluate the limit, if it exists x² + 9 – 5 30. lim x→-4 x + 4

A:

Q: Evaluate the limit, if it exists. 2 - x² – 16 lim X-4 x – 4

A:

Q: Use the formal definition of the limit to prove the statement rigorously.

A: To prove: limx→0x2+x3=0. We know that limx→afx+gx=limx→afx+limx→agx Therefore,…

Q: Draw the graph of f(x) = E, and annotate the graph to indicate the meaning of I-2 lim - 2| T→2 x – 2…

A: We have to find limit

Q: Find the indicated limit, if it exists. x+4 x<-5 lim f(x), f(x) = X-5 4 - x x2-5

A:

Q: lim X + Jx2-4x tト X->

A: Given, limx→-∞x+x2 -4x+1          We have to find the value of limit

Q: Find the limit. lim V+3

A: Given query is to find the value of the limit.

Q: Evaluate the limit x2 + 3x – 18 lim x-3 x - 3 Enter I for o, -I for -o, and DNE if the limit does…

A: We find limit of given rational function

Q: A- The result of the following limit is 2x² + 3x lim xx0x³ + x + 1

A: The objective of the question is evaluate the limit .

Q: lim x2 - 4 x→2 x – 2

A:

Q: Use the precise definition of a limit to prove the following limits. Specify a relationship between…

A: To Prove - limx→3 x2-7x+12x-3 = -1Cosidering LHS - limx→3 x2-7x+12x-3 = limx→3 x2-3xx-4x+12x-3limx→3…

Q: Find the limit, if it exists.

A: To evaluate the limit: limx→-∞x3-4x2+1. Evaluating the limit.…

Q: Evaluate the limit, if it exists. (If 1 2 lim (x + h) h-0 h

A:

Q: Find the limit, if it exists

A:

Q: Find the following limits if they exist. a) lim xx* +1-x)

A: Given limit can be simplified as

Q: Find the following limits: x2 +x - 6 lim x-2 |r - 2| lim x2 - 4 Note that the second limit above is…

A:

Q: (b) Find the following limit: 4x +5 lim x+2 2x -1 (i) (ii) lim 4 x+* x* -x' +2

A: The solution is given as

Q: Evaluate the limit, if it exists.

A: Given,  limu→24u+1 - 3u - 2 When we apply the limit directly into the function we will get 0 in…

Q: Evaluate the limit, if it exists.

A: Given limit limx→5 x2-3x-2x+6x-5limx→5 xx-3-2x-3x-5limx→5 x-3x-2x-5

Q: 10. Find the value of the limit or state that it does not exist c) lim f(x) = X2"

A:

Q: Find the limit if it exists. x²+5x+6 Lim,→-3 a+3

A:

Q: find the limit, if they exist.lim x-&gt;a (x^2+x-6)/x+2

A: Here, two cases arises, if a=-2 ,then denominator of function is zero and limit does not existIf a…

Q: # 11. The lim,→-4 x²+ cx+c+5 x² + 5x+4 exists. What is the value of “c“? What is the value of the…

A: