) Find the value of k that makes function continuous at ¤ =4 f(x) = { | 2x +7 > 4 6x -k < 4 (i) If lim f(x) = 18 and lim g(x) = 27 then find lim[3f(x) + 6g(x)] %3D %3D Sæ – e3z I<0 ( ii) Determine whether the function f(x) = is continuous at = 0. 3x – 1 -

Q: xn+1 – 1 - Show that F(x) is an antiderivative of y = x" for n +1 n + -1. Then use L’Hôpital's Rule…

A: Given:           F(x)=xn+1-1n+1, n≠-1 To show: 1. F(x) is an antiderivative of y= xn  2. limn→-1…

Q: 4. Sketch the graph of a function that satisfies ALL of the following conditions: ➡D: {X ER | x #4}…

A: Solution :-

Q: 5. Let {(2) = { * * x + 0 x + 2 x = 0 and o(e) = { * *' x + 0 x = 0. x +1 g(x) i. Show that lim,→0 =…

A: find the limits as follows  limx→0fxgx=limx→0x+2x+1=21=2 limx→0fxgx=2 now limx→0f'xg'x=limx→011=1…

Q: Find the limit. x – x3 lim x→0 x2 + 1 Using infty for o. O -1 O DNE O infty O -infty

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Q: 4. Determine whether the functions f are continuous at given points: x+2 S(x) ={ x +x-2 0, x=1 at x…

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Q: 9. Verify the existence of limit as x approaches to 0. Sx+1 , x>0 lu-1 , x< O lim f(x) = -1; lim…

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Q: 6. Find the limit of f(x) = -- 10 as x approaches co and as x approaches - c lim f(x) = X00 (Type a…

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Q: a f'(x) >0 on the interval (0,2) b) lim f(x) # 1lim f(x) メう2+ C)f"(x) < 0 on (3, 5) d) f is…

A: Interpret the graphical meanings for the given condition. The derivative f’ (x) is greater than 0…

Q: 1 Is the function given by f(x) = ! x+1, for x 2, Choose the correct answer below. O A. The given…

A: We have to find

Q: 1. Evaluate the ff. limits: -1 (e*). V1 – e2¤ sin' 2 lim (а) x→0- - 1 - (b) lim x + sin

A: Explanation of the answer is as follows

Q: 1. Solve the following limits. (a) lim 1-0 V1+ x² x In x (b) lim 1400 x + In x 2+ sec (3x) (c) lim…

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Q: Əsoddns f(x) is a continuous positive function, and n 2 2k Sn Es(1+ k=1 a Riemann Sum (with…

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Q: a. Find the Domain for y = = /4 -x + ! b. For what value of (k) is the function y-f(x) continuous at…

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Q: _11. If lim (x² +1) = 2, and x = 2.5, then x->-1 lim (x² + 1) is equal to. x-2.5 A. 5.25 C. 6.25 B.…

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Q: 19. Using the l'Hospital's rule to find the limits e3r – 1 In(ln æ) 1 e" – 1- x – ² (a) lim a→0 In(x…

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Q: For what value of the constant c is the function f continuous on (-o, 0)? cx2 + 3x if x < 2 f(x) =…

A:

Q: -1– x + 5 if x - 2 Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: limx→-2-f(x)=6, limx→-2+f(x)=6,  and limx→-2f(x)=6

Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)(0,0) f(x, y) does not exist by using…

A: Note: if a limit exists at a point,it must be the same limit along any path approaching that point.…

Q: lim, f(x)=5 lim f"(x) = 4 16 - what is the following limit value? f(x- 2)-x lim x- 5 O A) 6 OB) 3…

A: Given:     To determine:

Q: 1. Find the limits lim (3x – 1) x-1/3 a) | cos x b) lim x 1 - T lim y--5 5 - v c) 3h +1 - 1 d) lim…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: f(x) = { S -4x? + 4x for x 0. According to the definition of the derivative, to compute f'(0), we…

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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)…

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Q: For the function f(x) = arctan 1 which is graphed on desmos. (a) Compute lim f(x) (b) Compute lim…

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Q: please answer parts a, b, and c

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Q: x' + 2, if x 0 (a) Find lim f(x).

A: Since , the only point of discontinuity can be zero . For rest of the points on ℝ the function is…

Q: a. The number L is the limit of f(x) as x approaches c if given any ɛ > 0, there exists a value x…

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Q: Determine if this function is continuous at z = -1 f(1) I -1 where f (x) = I+2 and g (1) = - +3z +…

A: NOTE: Refresh your page if you can't see any equations. . here we want the left-side limit at x=-1…

Q: Explain why or why not Determine whether the following state-ments are true and give an explanation…

A: Since you have posted multiple questions ,we solve first 3 questions for you .To get the remaining…

Q: Please show step-by-step solutions

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Q: (a). Determine the interval(s) on which f(x) = is continuous. (b). Find lim analytically. 9-1 3 -1…

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Q: 2 — х — г? if x 5 - Calculate the following limits. Enter "DNE" if the limit does not exist. lim…

A: Here we will find the given limits,

Q: 3. What is lim f(x)? lim f(x)? Why? 10+ 8. 6 4 2- -5 -4 -3 -2 -1 2 3 4 4. What is the limit of lim…

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Q: 37. The function / has a removable discontinuity at z„. Therefore A S(7,) exists B lim f(z) exists C…

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Q: 11) lim -3sin (x)= X→ +∞ A) 0 B) +o C) DNE D) 1 12) Use SPECIAL LIMITS and SQUEEZING THEOREM to find…

A: We expert are following guidelines.We are supposed to do first question. Kindly repost the second…

Q: #2: Consider the function f(x) = and the limit lim f(x). x + %3D x→1 (a) Find the maximum value of d…

A: see below the answer

Q: M 27. (a) By graphing the function f(x) (cos 2x- cos x)/x %3D and zooming in toward the point where…

A: Given function f(x)=cos2x−cosxx2

Q: Please I want solution of sub-parts question 5 with step by step. Many Thanks

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Q: -1 sx3 O A) -0 O B) -1 O C) 7 O D) Does not exist

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Q: Find the following limits of x2 – e5a 5а — 1 x 0 (i) lim f(x) (ii) lim f(x) x→0- (iii) lim f(x)

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Q: 45. a) Find lim h(x). b) Find h(1). c) Is h continuous at x = 1? Why or why not? d) Find lim, h(x).…

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Q: Evaluate the limit lim Eƒ(ci)Ax¡ over the region bounded by 3%3D1 n-00 the graphs of the equation f…

A: To: Evaluate the limit limn→∞∑i=1nf(ci)∆xi over the region bounded by the graphs of the equation…

Q: 8. Find the area of the triangle formed by the x and y-axes and the tangent to the graph of y =. %3D…

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Q: f(x) =  x2 + 1    if x < 1 (x − 3)2    if x ≥ 1. (a) Find the following limits. (If an answer does…

A: Explanation: Given that,  f(x)=x2+1if x&lt;1(x-3)2if x≥1 Firstly find the Left-hand limit(LHL) and…

Q: Find the limit of f(x)

A: Given information

Q: 2. Use the given values to set up a table to evaluate the limits. Round your solutions to sin 3x…

A: limx→0sin3xx

Q: S2 – x – x² if x 2 - Use a graph to determine the following limits. Enter DNE if the limit does not…

A: The graph is shown below:

Q: O3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x→0 sin4x 2- lim…

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Q: A function y = f(x) is defined and continuous for all x. This function satisfies all of the…

A: Given that the function  y=fx is defined and continuous for all x. Solution (a): According to the…

Q: x+4 Which will prove that f(x) is continuous at C= -4? x2+16 1. f(-4)=0 II. lim f(x)=0 III. f(x)=…

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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.