Assume that if lim f(x) = L, then lim cos f (x) = cos L. In each x→a case evaluate the limit or indicate that the limit does not exist. 2x cos x (b) lim x→1/2 (a) lim cos 1— 2х 1– x2 | (c) lim x' cos(1 – x) (d) lim - 1- cos(x2)

Q: lim f(x) f(c) a) lim f(x) 1 DNE x--3 b) lim f(x) DNE 1 x-1 c) lim f(x) -1 -1 d) lim f(x) e) lim f(x)…

A: Graph of the function is given.

Q: * -x+1 if x1 (a) The value f(1) does not exist, while lim, 1 f(x) exists and equals 1. Doth f1).

A: f(x) = x3-x+1 if x<1        = 1/x        if x>1 Since the function f(x) is not defined at x= 1…

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A:

Q: 1 1 (b) lim x-0 'tan x e* – 1 -

A: =?

Q: 3) If the lim f(x) = 2 and lim f(x) = -1 %3D x-3- x-3+ Then what is the lim f (x) = x→3 %3D a) Why?

A: To find the limit of the f(x) at x=3

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A: Given limx→0 x cosec x .sec x⇒limx→0 x.1sin x.1cos x=limx→0 2x 1sin 2x

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Q: Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6  f(x) = L, and prove that the limit…

A: Let f(x) = (3x^2 + 16x − 12)/(x + 6). Find L such that lim x→−6 f(x) = L, and prove that the limit…

Q: Calculate the limit

A: limx→∞ arctanx2+99-xApplying Chain rule: =-π2limx→∞ arctanx2+99-x=-π2  Decimal:   -1.57079…

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A: Explanation of the solution is given below...

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Q: Let F (x) = { tan (x − 3) x < 3 x-5 3 ≤ x Then lim F(x): x 3- = CH M₂ 146

A:

Q: 3 - – If lim f(x) = 3.5 and lim,-2+ f(x) = 6. 5 , the function has a double sided %3D x→2- limit or…

A: Given,          limx→2-fx=3.5 and limx→2+fx=6.5We know that,           Condition of double sided…

Q: Find the limit

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Q: Sketch the graph of a functionf that satisfies all of the given conditions: 1) f(0) = 1, f(2) = 3,…

A: Graph is given below:- You can verify all the conditions.

Q: if f(x) True = False 1 {} if x # 0 if x = 0 2 then_lim ƒ(x) = 0 x 0

A:

Q: lim ←x sin²x x- x - 13 ㅠ 311

A: For the following limit, to find a number  and a function  such that thelimit equals .

Q: Find the limit or determine that the limit does not exist limx→2 (sin(pi/2 times x)/cos(pi times…

A: We have to determine whether the limit exists or not for the following expression…

Q: 2. Use the graph in Fig. 11 to determine the following limits. lim f (x) lim f(x) lim f (x) (b) lim…

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