(b) Assume that lim,6 f(r) = 9 and that lim,6 g(r) = 3. Compute lim f(r)g(r) - f (x)f(x) + g(x)g(x)

Q: Show that lim (x,y) →(0,0) 16x4 +9y¹2 4x² + 3y6 does not exist.

A:

Q: 2) Show that the_lim. 1) xy2 lim (x,y)→(0,0) x² +y²

A:

Q: Suppose that lim 4f(x)+ 2x – 14 5. Find lim f(x). z→1 %3D z→1 x – 1

A: Given

Q: 2. Use the definition of the appropriate limit to show (a) lim→∞(2x² + 4x – 1)/(3x³+ 1) = 0. (b)…

A: a) Given limx→∞2x2+4x-13x3+1

Q: Find the limit (if it exists). If it does not exist, explain why.

A: Given: gx=1-x,       x≤1 gx=x+1,          x>1 The limit limx→1+gx is the right hand limit at…

Q: What is lim1 f (x) ? X

A: Find your answer below

Q: 1. Use the definition to show that x² - y² lim (x,y)→(0,0) x² - y² = 0.

A:

Q: Find the limit analytically: 2-4x lim 40 5+3x 1.

A: Solution is here

Q: Consider f(x)=x−9/x+4 a) As x→∞, f(x)→ b) As x→−∞, f(x)→ f(x)=10x+7/x−6 c)limx→∞f(x)=

A:

Q: Find a Limit using factoring:

A: We have to find the limit using factoring: limx→1x2+2x-3x-1 This is 00 indeterminate form of limit.…

Q: Prove using formal definition. (a) lim x→0+ 1/x = ∞.

A: Draw the graph of the function .

Q: Show that lim (x,y)→(0,0) 16x4+9y12 4x²+3y6 does not exist.

A:

Q: What is lim f(x)? X-1

A: Given graph: To Find: limx→1f(x)

Q: x² – 1 lim x→1 x – 1

A:

Q: (b) Prove that lim,→20,¤€A ƒ (x) exists and is equal to lim→0 Yk-

A: This problem is related to the sequence of functions. Given:  fkk∈ℕ is a sequence of functions from…

Q: Let f(x) = x/(x + 1). What is lim, »f(x)? How large does x have to be so that f(x) > 0.99?

A: Given:            fx=xx+1 Find: limx→∞fx=limx→∞xx+1

Q: Compute

A: The limit of the function is the value of the function when the value of the arguement is…

Q: If −x2 − x + 1 ≤ g(x) ≤ x2 − x + 1 for all x does not =0, what is lim x→0 g(x)?

A:

Q: If ƒ(1) = 5, must limxS1 ƒ(x) exist? If it does, then must limxS1 ƒ(x) = 5? Can we conclude anything…

A: A function f(x) is said to be continuous at a point x = a, in its domain if the following three…

Q: V2x -1 Using defination of limits, prove that lim Jx- 3 L^ = x4

A:

Q: a. Evaluate limx→5 f(x), where f(x) = { 11x+ (2 +77) Ef x5 f(x) exists.

A: solution is given below..

Q: Find a number b such that lim- .2. x²-4 =2 x-b x-x -2

A:

Q: -f(x): a. lim

A: We'll answer the first question only since the exact one wasn't specified. Please submit a new…

Q: 5. If lim f(x) = 8 but lim f(x) does not exist, what can you X+2+ X+2 say about lim f(x)? X2-

A: We know that, limx→afx=l, if: limx→a+fx=limx→a-fx=l

Q: Calculate the limit algebraically: x³ + 8 lim x→-2 x² + 7x + 10

A: Consider the given expression, If we substitute  in the expression we get  form. so, use L-hospital…

Q: find the lim as x approaches infinity where

A:

Q: Use lim f(x) = -2 and lim g(x) = 5 to find the limit. %3D lim [3f(x) – 4g(x)]

A: The given limits are limx→cf(x)=-2 and limx→cg(x)=5

Q: . Is it possible that f(2) = 5 but limx→2 f(x) = 7? If so, what kind of function can satisfy this?

A:

Q: Find. 1) a. lim f(x) and b. lim f(x). 3- 4-

A: Answer and explanation is given below..

Q: Find the limit: limx 1(x2 + x + 2)/( x + 1)

A:

Q: Find the limit analytically: 2-4x lim- 40 5+3x 1.

A:

Q: Use the theorems to evaluate the limit. 1 lim x → ∞ x2 ||

A: We have to evaluate the limit.

Q: Use the theorems to evaluate the limit. 1 lim x →∞ X² ||

A:

Q: Let f(x) = Vx - 1 if x>4 and f(x) = x² – 4x + 1 if x < 4. Find: %3D lim f(x) x→4

A:

Q: Evaluate the limit  Limx-&gt;0 (ex-1-x)/x3

A:

Q: Determine the value for c so that lim f(x) exists. x-3 f(x) = 5**, *+c, for x 3

A:

Q: The function f(x) of the below graph is discontinuous at x = -1 because: a) f(-1) does not exist b)…

A:

Q: Suppose limy-e- f(x) = I and limx-e- g(x) = m. Prove that limxe-(3f (x) + 4g(x)) = 31 + 4m.

A:

Q: Calculate the limit algebraically. lim (x +2) O -2

A: Given limit is  Since the function f(x)=x+2 is defined for x=2, therefore, we will evaluate the…

Q: Determine the value for c so that lim f(x) exists. X-3 f(x) = +c, for x3 The value of c is.

A: Topic = Limits

Q: —ах+6 if x2-1 Let f(x)=< For what value of a does 2x2 +ах ifx<-1 lim f(x) exist? x--1

A:

Q: Suppose that lim as x approaches infinity of f(x) + x^2 = L for some number L. Then lim as x…

A:

Q: Prove, using the formal definition, that lim,→1- V1– x = 0.

A: Given, limx→1-1-x=0

Q: Find the specified limit. f(x) - x+2, x > -1 lim f(x) ?

A: The given function is            f(x) = x2,  x&lt;-1x+2, x&gt;-1 We have to find the following…

Q: Find the limit. (- 3m=) lim In x x→0+

A:

Q: lim(x,y)->(0,0)  (4x2y)/(x2+y2)1/2

A: Given: lim(x,y)→(0,0)4x2yx2+y2         (1) To compute: The limit.

Q: Find the limit x lim- +x+2 X + x +1

A:

Q: Use the definition to show that x² - y² lim (x,y) →(0,0) x² - y² 0.

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.