3. Let f(x)=x² +4 and g(x)=3x. Find the limit. lim g(f(x)) A) 189 B) C) 75 87

Q: (1+ h)² – 1 - Evaluate the limit: lim h

A: Recall: A Limit is the value that a function approaches as the input approaches some value.

Q: Compute the limit, or show that it does not exist: lim (x,y)→(0,0) x³y? + x²y³ x4 + y4

A: To Determine :-  Compute the limit or show that it does not exist : lim x , y →  0 , 0 x3 y2 + x2…

Q: Evaluate this Limit

A: Consider the limit

Q: Find the limit if it exists, or show that it does not exist. lim (z,9)¬(0,0) zª + 4y²

A: Given:

Q: Evaluate the limit. lim f(r), f(a) = x² - 4.x 4, x -1 -2, x = -I C3= O -5 O-9 O-1

A: Topic = Limits

Q: What does the limit notation lim f(x) = L mean?

A: Given, limx→af(x)=L

Q: Use the definition of the limit to prove that lim (r+2y– 1) = 1. (7,4) (0,1)

A: Given function is fx,y=x+2y-1

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: Given that lim f(z)=-10, lim g(z) = -2, lim h(1) = 8, find the following limits Enter inf for 00,…

A: As per our guidelines, I can answer maximum three subparts of a question. To know rest, please…

Q: evaluate the limit using the Basic Limit LLlws and the limits lim xPfq = cPfq and lim k = k.…

A:

Q: find the limit or explain why it does not exist. lim In (t – 3)

A: limt->3+ln(t-3)

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 limit, if it exists. (If an answer does not exist, 3 - xy ху lim (x, y) → (2, 1) x² +2 +9y²

A: We will apply the limits.

Q: Evaluate the limit:

A: We have been given the limit limx→cxp/q=cp/q

Q: evaluate the limit or determine that it does not exist. lim(x,y)→(−3,−2)/(x2y3 + 4xy)

A: To find limit  limx,y→-3, -2x2y3+4xy

Q: Use the Squeeze Theorem to find the following limit when b − |x − a| ≤ f(x) ≤ b + |x − a|. lim x->a…

A:

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: To evaluate the given limit substitute x=3 and y=2 in the given function.

Q: Evaluate the limit using the Basic Limit Laws

A: Given, limt→-1t2+1(t3+2)(t4+1)

Q: Prove, using the e-8 definition of limit, that: (a) (b) lim ²+1=2 24-1

A:

Q: Step by step

A: Plug x=infinity

Q: Evaluate the limit or state that it does not exist for the figure given below:

A: Evaluate the limit of the given function.  as the given function is in 0/0 form so apply the…

Q: Evaluate the limit lim z→2+i [(z−1)(3−2i)+1−3i] and use the definition of the limit (−δ) to…

A:

Q: Evaluate the limit given limx→c f(x) = −6 and limx→c g(x) = 1 /2.

A: Given  limx→cf(x)=−6limx→cg(x)=12

Q: lim (1+e 9)º

A:

Q: 1 lim ty1 + t

A:

Q: t2-3t+5 lim -1+ 0 t

A: Given:        limt→0et−1t+t2−3t+5t2−1

Q: Evaluate the limit lim, 5 a. 2 b. 0 C -1 x d. I

A: Given: limx→5 x+11x-1

Q: Use the e – 8 definition of the limit to prove that lim x2 – 2 = 2. %3D - x→2

A:

Q: 8. Evaluate the limit lim A) B) 1 C) D) E) 23

A:

Q: Find limit, or show that it does not exist. 2x²y (x,y)¬(0,0) x*+y2 lim

A: Consider the given: limx, y→0, 02x2yx4+y2Find two different paths to approach the point that gives…

Q: Evaluate the limit using the Basic Limit Laws

A: Given: Let y=limt→43t-14t+1 To Find: To evaluate the given limit.

Q: Evaluate the limit given limx→c f(x) = −6 and limx→c g(x) = 1 /2.

A: To evaluate: The limit limx→cfxgx. Given: The limit limx→cfx=-6 and limx→cgx=12. Concept used: The…

Q: Evaluate the limit, if it exists.

A:

Q: Find the limit: lim (x,4) → (5, –1) g4 + v2 %3D

A: We know that if a function f(x,y) is continuous at a point (a,b) , then lim(x,y)→(a,b)f(x,y)=f(a,b)…

Q: Let ƒ : (a,b) →R  be an uniformly continuous function. Finish the proof by showing that the limit…

A:

Q: Use the definition of the limit (e – 8) to show that 1 lim - = i. 2+-i z

A:

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

A:

Q: Use the Properties of Limits to evaluate the limit, if it exists. (If an answer does not exist,…

A:

Q: Find the limit. lim V+3

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

Q: Use formulas (3)–(5) to evaluate the limit.

A:

Q: Let f(z)=z2 - 7z+10 the find lim(zk )f(z)=?

A:

Q: Given lim f(x)=L, Im fx)=L, and L, =L, 1. lim f(x)=L, II. lim f(x)=L, III. lim f(x) does not exist

A:

Q: Find the limit L. Then use the e-8 definition to prove that the limit is L. lim (x + 8)

A:

Q: Evaluate the limit L, given lim f(x) = -12 and lim g(x) = 3 %3D %3D lim [f(x) + 3g(x)] L = 1.

A: Solving by limit property

Q: Evaluate the limit, if it exists.

A:

Q: Find the limit, if it exists, or show that the limits does not exist. a) lim (x5 + 4.x³y – 5a²).…

A: Given lim(x,y)→(5,−2)(x5+4x3y−5x2)

Q: Determine whether the limit exists. If so, find its value. If the limit does not exist, indicate…

A: Let L is the value of given Limit.

Q: Find the limit L. Then use the ɛ-8 definition to prove that the limit lim V6x x→0 L =

A: Here we have to find the limit L=limx→06x3

Q: Evaluate the limit: lim h→0 (−5+h)² - 25 h

A:

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.