Example Let sinh(2)e f(2) Find the residue at z = 0.

Q: cosh 1+j T 2 * T sin 1-j- 2

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Q: (а) lim 1-cos() 3x 1/х 1/х (b) lim хе 1/х (Hint: хe x+0"

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Q: ELIMINATION OF ARBITRARY CONSTANTS

A: The given solution curve is y=C1excosx+C2exsinx=ex C1cosx+C2sinx. That means, the roots of auxiliary…

Q: d) lime tan 0 sin 0 3. e) lim0 sin z-cos z+1 3z

A: We have to find the limits .

Q: Find the limit.

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Q: 1-sin t lim 1+cos 2t t- 2

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Q: lim (x)-(.0) tan , -= (A) Does not exist (B) e? (C) 0 (D) ezn (E) e *IN

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Q: 6. (a) f(x) = arctan (e-2) 6. (b) f(x) = [arcsin (²)]³

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Q: y=-sec^-2 (In x)

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Q: Suppose that a dimension X in the area A= 6x*2 of a shape are differential equations functions of t.…

A: Here we differentiate the function with respect to ' t '

Q: sin 2n x Prove that: dx = 0 for all n e N. sin x

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Q: EXAMPLE 2 (a) What is the maximum error possible in using the approximation below when -0.2 < x <…

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Q: II. Perform the integration. sinh (e-") dx e² cosh(e-¤) 4.

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Q: Example 6.24. Show that we cannot use L'Hopital's Rule to evaluate x sin- lim X0 sinx itel'e Pule we…

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Q: Question 1 (The Substitution Method for Indefinite Integrals). Calculate dr.

A: here we need to find the integration using substitution method.

Q: e) lim 1-cost sin²)

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Q: c Functions. Prove the identity cosh x – sinh x = e x-

A: We have to show the given condition

Q: |- lim メ→ X-3 2. lim メ→2 (会 4 メー2 メ*-4 3. lim メ→。 3メ - S;u4X 4. lim メ→。 tau3X 5- lim 1- Cose Sin'e

A: Since you have asked multiple questions. So, we are solving first few for you. If you want any…

Q: (z-2)(z-2) lim log1/3 sin((2z+ 1)(z-2)). Z→+2

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Q: tan x 2. (a) lim e →号一 (b) lim sin (tanh 3x) エ→十0

A: limx→π2-etanx

Q: 71. Prove the reduction formula tank x dx = tan" k-1 х | tank-2 x dx k – 1 Hint: tank x = (sec² x –…

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Q: tergal / 1 dx using the residue theorem. (x2 + 1)3

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Q: sin(4z) f(x) = 9x 0.4 0.35 0.3 0.25 0/5 -0.25 0.25 sin(4x) Evaluate lim 9x Enter at least 3 decimal…

A: Let's find.

Q: sin a COS T Solve by hospital rule lim-

A: after solving we get limit is 1/3

Q: 5. Find the length of the curve x =y? +2} from y =0 to y = 3. In(5x+2). In 3x 6. Solve lim

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Q: 1. Approximate sinh(0.6) using the third degree Maclaurin polynomial of sinh r.

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 57. Extension of Example 8 Show that cos (x) is dx sin (x). 180

A: The objective is to show that ddxcosx° is -π180sinx°. The function cosx° is given in degrees bu the…

Q: 7. lim a sin(1/a) = %3D a-0+

A: Given lima→0asin1a

Q: Example 2: Consider a pond that initially contains 10 million gal of fresh water. Water containing…

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Q: Let f be a function with f (3) = 1 such that all points (x, y) on the graph of f satisfy the…

A: This is Separable differential equation

Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: OForm patial differential equation by elinsinating arbitrary functions f and g from 2 = f) +y9(x) a)…

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Q: Evaluale lim t+s iHexists.

A: We need to find limt→-1t+1t+1 Now, x=x , x&gt;0-x, x&lt;0 Therefore,  t+1=t+1      , t+1&gt;0-t+1 ,…

Q: A)) Q1/ Find Fourier Sine Integral presentation of the function: f(x) = xe-* , x>0

A: The given function is: f(x)=xe-x ,      x&gt;0

Q: log3 (2r² + y) + tan (2-³) = sin-¹ (²-1) +

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Q: 10. lim ) 1 -1) A-0 hV1+h sin x 13. lim 0 2x-xr V8+x -2 (Hі 16. lim

A: We have to use proper techniques here.

Q: 2. Let f(x) = -x³ - cosx and po = -1. Use Newton's method to find p2. Could po = 0 be used?

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Q: lim E(cos (27x;))Ar over [0,5] COS i=1

A: The definite integral is defined as  ∫abf(x)dx=limn→∞∑i=1nfxi*ΔxWhere, Δx=b-an, xi*=a+iΔx The…

Q: 2-t+ sint 45. lim t+ cos t

A: We have to find he limit: limt→-∞2-t+sin tt+cos t

Q: = sin? (esin" t) + cos-1(2t3 (x) = tanh-1 x + In V1– x2 |

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Q: (1) limr-(n/2)-(tan x)cos x (2) lim,-o x-3(tan-x-x) (b) If у %3D 4u?-Зи + 2 %; и 3 е* + 2e2х, find…

A: For other questions reupload according to bartleby guidelines

Q: Find the limits

A: Given,                     lim(x,y)→(0,ln2)ex-y     And we have to find its limit.

Q: Using Fourier Series D (1) Sin (wot) 2 Siu (wot) Cos(wot) Find

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Q: COS 9. Prove cost - sin* t =1 - cos t - tan²t

A: We have to prove that  (cos4t - sin4t ) /cos2t  = 1- tan2t

Q: S lim 1 (1+x)2+n³ cos (nº + x³) dr

A: HINT:  Used Integration formulas and limit formulas.

Q: 3. f(x) = tan + 1 Period: 3 Positive Asymptote: Negative Asymptote: y-intercept: 1

A: Consider the function  f(x)=tan32x+1