DIScuss, w/o function IS graphin9,1f the following continu ous at x=0 f (x) = %3D 1X1 -(US x If x70 -CUS If you think fis not cuntinuous at what Kind of dise continuity xzo,

Q: (a). Simplify the indicated limits on the following. (CLO-2: LOL: C-4, PLO- 1). (i). lim (i). lim…

A: Since you have posted multiple questions but according to guidelines we will solve first question…

Q: You will find a graphing calculator useful for Exercise

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A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

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Q: (b) Here are graphs of solutions of the above equation on [0, T]. While most solutions tend to +∞ or…

A: (a)   Given differential equation is         dydx+cot x·y=1       Integrating factor is…

Q: (2x² +3 x1 verifying the three conditions needed for continuity at a point. x(x² – 9) (x² – x)(x+ 3)…

A: To check continuity at any point x=a we have to check L.H.L. =  R.H.L. = f(a).

Q: A. Directions: Find the limit of the following rational functions: X-1 1. lim x1Vx² + 3 sec x 2. lim…

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Q: Ise e-8 proofs to show that; OIf f(x) = Vx, then lim f(x) = va, where a > 0 %3D %3D

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: What is the value of the limit below? (e2-1-2x)(3x - sin lim (3x)) Hー0 25

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Q: V. Show that Зx? — 6х — 9 lim 3- х X-3 Is continuous or discontinuous at x = 3

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A: We have to evaluate the following limits -  lim(x,y)→(2,0) xy - 2yx2 + y2 - 4x + 4

Q: AP(8) x-1 c) Let f(x) = which x approached zero. x+0. Find by using numerical calculations in a…

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Q: S(-1-2)² +5 if z+ Let f(1) 4x + 13 if a = - 2 %3D Calculate the following limits. Enter "DNE" if the…

A: see below the answer

Q: 1. Solve the following limits. (a) lim II 1+ r? x In x (b) lim 2+ sec (3x) (c) lim /6 tan (3r)- 1

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Q: Indeterminate Form 12. lim tln 1+ X- 13. lim [w² In(4²)] 14. lim[e* +x] 15. lim[cos2y] yo* x0*

A: Solution is given below...

Q: A graphing calculator is recommended. Use the Squeeze Theorem to show that lim (x² cos(18nx)) = 0.…

A: To use squeeze theorem to show that

Q: 2.a?y Using paths, show that the following limit does not exist. lim (x,y)→(0,0) 3x4 + y?

A: According to the given information, it is required to show that limit does not exist.

Q: Which of the following statements is true? 7x2 7 A lim 3 (ку) - (0,0) Зx2 — 5ху+ 2у Зx+у-4 lim 8…

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Q: 4:35 Cancel Done 2x-7x+6 O LIVEGiven f(x) = %3D x-2 (a) Find limf (x)analytically (i.e. using…

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Q: 3Cos-3 Cos 0 Use l'Hôpital's rule to find the limit of lim 50

A: Given,           limθ→03cosθ-35θ

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Q: 10 -10 At what values of x does ƒ (x) has an infinite limit (as x approaches this value)? Write down…

A: Given: To find at what value of x does f(x) has an infinite limit.

Q: In Exercises 11–18, use the function f defined and graphed below toanswer the questions.   (a) Does…

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Q: ax? + 15x + 15 +a lim X--2 1) Find value a such that exists. Then find the value of the x2 +x- 2…

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Q: Evaluate the limit, 1 (x + h)² lim

A: limh→0 1(x+h)2-1x2h

Q: valuate the limit 8x2 – 9x – 9 lim x→-o 7 – 7x – 10x2 E the limit does not exist enter DNE. imit =

A: We have to find limit

Q: hesaplayınız. tan tdt a) lim 140 7x b) lim In x e e-x-1 c) lim cos x-1

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Q: 6. Calculate the value of each limit (possible answers are a number, plus or minus infinity, or…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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Q: (2 - a - a2 if a 3 Calculate the following limits. Enter "DNE" if the limit does not exist. - lim…

A: Find right hand limit and left hand limit, then check these are equal or not.

Q: %3D The slope of a tangent line to f(x) at x = a can be found using the formula lim fx) - f(a) X - a…

A: fx=xa=36fa=36=6

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Q: Question L'Hopital's Rule can be used on which of the following limits? Indicate all the apply.…

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Q: QI:B/ Use l'Hôpital's rule to find the limits In (csc x) lim xn/2 (x - (7/2))?

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Q: (ex-1)sin(2x)2 x(1- cosx) Evaluate the limit lim Select one: None of them 4 8.

A: Given,  limx→0ex-1sin2x2x1-cosx  We have to evaluate the limit.

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A: Given query is to prove the limit expression m

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Q: (6x -1 x² +8 having limit atx = k. Find the value of k. x> k) D: If the function f(x) = %3D

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Q: (C may use any theorems we have proved in class or on homework. -) Calculate the following limits,…

A: Since you are asking question with multiple subparts. We are answering only the first three subparts…

Q: Consider the function fix) - sin x. Complete the table below and sketch its graph. 011/6 11/2 Sn/6…

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Q: х3 — 4х? 8(7x – 4) (x + 2)* x(х + 8)(х — 2) | Given: f (x) : with f'(x) ,аnd f" (x) - %3D (x + 2)2…

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Q: Consider the function fix) - sin x. Complete the table below and sketch its graph. 011/6 11/2 5n/6…

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Q: Evaluate or show it does not exist a) lim 2 (xy.2)=(5,2,-3) arctan(*) b) lim 2xy (x,y) →(0,0) x²+2y?

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Q: Fact 1: | arctan t<14 for any real number t. Fact 2: t <14 for any tE (-1, 1]. (a) Prove by using…

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Q: You may assume that the exponential and cosine functions are continuous and may freely use…

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Q: 2x Sí“(2t-2)² dt (a) Find the limit (if exist): lim 1 2х-1

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