0, Let f(x) sin, x> 0. y [o, y sin, x>0 -1 a. Does lim,-0+ f(x) exist? If so, what is it? If not, why not? b. Does lim,0 f(x) exist? If so, what is it? If not, why not? c. Does lim, 0 f(x) exist? If so, what is it? If not, why not?

Q: 1-cos(0) lim 02 e-0 1 lim (1 + x)a x-0 If f (x) is continuous at a, then what is the value of lim…

A:

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: 5 tan(4x) x→0 3 sin(2x) Evaluate lim using L’Hôpital's rule.

A: The  L'Hopital's rule is: Suppose, f(x) and g(x) are two functions and their limit is given as:…

Q: (z+2 z< 0 sin (x) 0<æ Let F (x) = Then lim F (x) =

A:

Q: 43. Assuming that lim 4 = 1, which of the following statements is necessarily true? Why? (a) f(0) =…

A: Consider a f0=0Here if x=0 , f0=0Substituting in limx→0fxx=00Inderterminant formDifferentiate…

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A:

Q: By using Sandwich Theorem, prove that lim sin x x-0 r

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A:

Q: Find the limit. lim (1+ sin(3x))/* x→0+

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: 2 dx In evaluating is same as evaluating lim cos ). Determine the value of f(x) if x=0.91 4 C- 2+

A: It is given that, ∫242xx2-4dxandlimc→2+cos-1f(x)c4 It is known that, ∫1xx2-1dx=sec-1x

Q: b) If x sin x 2 - 2 cos x hold for all values of x close to zero. Find limx0 xsinx ? 2-2cosx

A: Given, limx→0xsinx2-2cosx

Q: need helping finding the "?" values.

A: To show that: limx→0(x2cos13?x)=0 Also, f(x)=-x2g(x)=x2cos(13?x)h(x)=x2

Q: Prove that lim |x|sin(1/x) = 0.

A: We need to prove that limit of given function is zero.

Q: Determine if the following limit exists. lim (1,v)→(0,0) x6 + y? This limit exists because as you…

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Q: Let Fexy=4 Find Lim FAt and Lim FEX) X->2* 2 Does l tM fe) exist? Why zis FM cON tin-noss at X=27…

A: Answer

Q: 12, Show that the following limits do not exist. (а) lim 1 (x > 0), (b) lim (x > 0), x-0x2 x-0 Vx…

A: Given: d) limx→0sin1x2 to prove limit does not exist.

Q: x? + 4x – 21 - Calculate the indicated limit.lim If a limit does not exist then answer +o O, or DNE…

A: 1. L=limx→3x2+4x-21x2-7x+12  =limx→3(x-3)(x+7)(x-3)(x-4)  =limx→3x+7x-4  =3+73-4L=-10 OR by using L'…

Q: (3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge gained in…

A:

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: 1. Evaluate: lim x→2 (x^2 − 4x + 4)/(tan^2(x2 − 4))  2. Use the Intermediate Value Theorem to show…

A:

Q: Vx sin(1/x). 6. Let g(x) y=Vx /y=Vã sin х y=-VF a. Does lim,0+ g(x) exist? If so, what is it? If…

A:

Q: 0, 5. Let f(x) = sin, x> 0. . y = Jain . a. Does lim, 0 f(x) exist? If so, what is it? If not, why…

A:

Q: (-cx² + 2x, (sin x + cos x, x> n x<π 9) Prove that lim (x* sin+5) = 5 10) f(x) = What value must c…

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Q: (3) Using the appropriate approach covered in Unit 6 of this Course along with knowledge gained in…

A:

Q: Given that lim f(x) X+ 0 x2 1- explain why lim f(x)= ∞, x2 +7f(x)- sin (5x)+ 1 2- evaluate the limit…

A: We have to find the following

Q: Consider the function given below. f(x) = sin 0, 1 X+1 1 x < -1 x≥-1 Complete parts (a) through (c).…

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Q: * + 2, if x 0' (a) Find lim f(x). (b) Give a simple reason why f is discontinuous at 0.

A:

Q: 1. Find the limī lim In(sin x) X→π-

A:

Q: Let g(x) = Vĩ sin(1/x). y=V y-Vi sin 27 -가 y=-VE a. Does lim, 0 g(x) exist? If so, what is it? If…

A:

Q: . Does knowing that | sin (1/x)| < 1 tell you anything about lim (x,y)→(0,0) y sin -?

A: To find the limit of the problem

Q: Let  f(x)=sin(ln|x|). Justify whether limx→0f(x) exists. If it exists, enter the appropriate value.…

A: f(x)=sin(ln|x|). Justify whether limx→0f(x) Since sine is periodic, then it does not approach any…

Q: b) sin (2x) tan (5x) Find lim- (Can't use L'Hospital's Rule)

A:

Q: 30. Use the fact that lim x→0 sin x X = 1 (shown in video) to show lim x-0 1 - cos x X = 0

A: we will find the required.

Q: In evaluating 2dx E, is same as evaluating lim cos-¹(f(x)). Determine the value of f(x) if x=1.13…

A: Integration

Q: エ→2ー Prove that lim sin(1/x) does not exist. Lot II

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Q: f(x) Consider the function: 9 sec z 18--7 tan x 9(x) What is lim f(x). I 9(x) -? Note: For limits at…

A: I have given this answer in step-2.

Q: 3. Given the function: f(x, y) = for if (x, y) + (0, 0). x* + y" (a) Find lim f(x, y) along the…

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Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

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Q: Q1- Evaluate the limit :- 1- lim - ( - cos) (1+ sin ) ) (1 + sin±)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: determine the limit limh→0[(x+h)2-x2]/h by treating x as a constant. determine the limx→0cos(2x)/x…

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Q: Find lim 2x sin using the Squeeze theorem. x-0

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Q: 5. Prove that if lim g(r) = 0 then lim g(x) sin () = 0. %3D

A:

Q: Could you use L'Hopital's rule to solve the following question in its current form: lim,0+ In(x+1) O…

A: We have one of the following form limx→af(x)g(x)=00 or  limx→af(x)g(x)=±∞±∞  In these cases we have…

Q: Let ƒ(x)

A:

Q: Evaluate the limid lim X'sin t X→o sin x?

A: We have to find limit

Q: 2 dx In evaluating is same as evaluating lim cosF(x))lc. Determine the value of f(x) if x=3.22 xV x2…

A: Solve the

Q: -x + 1,x 2 0 Let f(x) = {x² + sin x -,x <0' (a) Find left-hand and right-hand limits as "x"…

A: Consider the given information:

Q: Use the limit lim 0-0 sin e 1 to find the value of lim 0-0 1-cos 0

A: Given limθ→0 θsin θ=1⇒ limθ→0 θ1-cos θ=00