elt is evaluated by using what formula? O et = cos(x) + sin(x)i O et = lim (1+ )" n %3D n→0 п et = lim (1 + *)" п O et 00 Σ j=0 j!

Q: no 2n? -5 sin( n) d] lim %3D 3. Prove or provide a counterexample for the follow

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Q: 2. (a) Use algebra to verify that (1+ (x – 1) (b) Differentiate arctan(x+1) – arctan(x- vital thing…

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Q: - 1 X If lim ([sin ¹x] + [2²sin ¹' (2x)] + [3³ sin-¹ (30)] x →0 X X + [x²³sin-¹ (x2x)]) + ... +…

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Q: Define ro = 0 and xn+1 = In chis to Newton's method. tan(r,)-1 sec2(z,) What is lim, Pn in this…

A: In the given question we have to find the limit of the sequence xn as n→∞ where the recurrence…

Q: 1- r + In (x) lim 41 1+ cos (3a x)

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Q: 4 35₂ In evaluating 2 dx X√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

A: We have to find the value of f(x) at x= 2.9.

Q: If L = lim x-18 x+ sin(+1) 1 + [x/³ ( and M = lim x→0 of L + M + 11. (172) 1 + 1² sin 2x tan-1 dt…

A: Here we will use L'hospital rule     limx→a fxgx  in 00 or ∞∞ form =limx→a f'xg'x   and Lebnize rule…

Q: Find the Wronskian for the set of functions.{x, sin2 x, cos2 x}

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Q: 1 Find Maclaurin polynomial P, to f (x )= : 1 1 cosx sin Ax 1-x 1+x

A: According to bartleby guideliness we can answer only the first three subparts of a question. kindly…

Q: 26. i) differentiate, with respect to x a) cos (2Vx) In(2x) b) 27. Differentiate y with respect to x…

A: See the attachment

Q: Which of the following may be solved by a direct application of L'Hopital's rule? sin 2x lim x→0-…

A: We have to check

Q: find the given limits

A: we have to find the limit limt→-1t3i+sinπ2tj+(ln(t+2)k

Q: ,3x lim x→0 CO cosh(Зa)

A: By substituting cosh(3x) in givenimit we can get the required value of Function.

Q: n+1 Evaluate lim cos“(x²)dx n→∞ (and show all work)

A: The required results are as follows: cos2 x=12+12·cos(2x) and cos 2x=1-(2x)22!+(2x)44!-(2x)66!+...…

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: Answer all the following 1- Find y" for y = x².tan-1x -1+cos2x 2- Find lim (by using L'hopital's…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Evaluate using the result of Exercise 54

A: Given: limh→0cos3h-1h2 we know that 1-cos2θ=2sin2θ…

Q: 4 35₂² In evaluating 2 dx x√√x²-4 is same as evaluating lim cos-¹(f(x)). Determine the value of f(x)…

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Q: e* – 4 , x< 3 - Let f(x) =- cos(x) %3D x2 3 lim f(x) = x 3 O DNE e3 – 4 - O 3 O cos (3)

A: Here we have to find the limit value.

Q: 5. Express lim 2 cos as a definite integral, then find t

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Q: 2y-n -Tt 7. lim cos y 2

A: Given:         limy→12π2y-πcos y    Let   π2-x=y, ⇒π-2x=2y      As y→π2,x→0

Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: * /Q3 e*-(x+1) lim X→0 CoSx-1 %3D -1 1 -2 O O O O

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Q: n lim >(sin (2mx;))Ax over [0,1] i=1

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Q: 2n3+n² sin(n)+6 48. Calculate lim,,→0 312 cos(m10n 19: (Proof is not required)

A: Use the algebra of limits to find the limit of the given fraction, and use a concept that limit of…

Q: Let a > 0 be real. Use residues to evaluate the princi- pal value of the integral R 1+ cos ax lim…

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Q: The Wronskian, W, of the functions y1 = sin(2x) and y2 cos(2x) is %3D

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Q: Find y' (y prime) and y" (double prime)y = cos(x2)

A: To determine the expressions for the first and second derivatives of the given composite function

Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: 1. Prove: a. S csch x = In|+ c b. S sech x = 2 Arctan(e*) + c

A: *As per the guidelines, only the first question is supposed to be solved. Please repost remaining…

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: sin 7Z „Find the residue of f (z)at z = 4 (z – 4)? Let f (z) =

A: Note:

Q: The limit lim (18 x; - 28 sin (x;)) Ax i=1 on the interval 0, is equal Tt/4 | (9 x² + 28 cos (x)) dx…

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Q: e sin a – x lim 10 10 cos x- 10 O - 0.2000 | O 0.1000 O - 0.1000 O 0.2000

A: Use L hospital's rule as it of indefinite form. So differentiate the numerator and denominator both…

Q: - Using any results from the course material, find the following limits: sin(x? – 9) а. lim x-3 (x2…

A: Solution:-

Q: lifferen tiake 3-Co5hx with respect to X 6+ sisht

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Q: Find the limits sin(3t) lim In(sin(3t)) i+ In(tan(4t))" j+tln(3t) A t→0 sin(4t)

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Q: Q2) A: If u = sin-()+ tan-(), prove that du ди x=+y дх ду = 0 ax ay n lim (1+ (1 + iV3)10 B: Find:…

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Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

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Q: Express the limit lim (3 cos (2ra* ) + 4)A¤¡ over [6, 8] as an integral. 2 CoS n- 00 i=1 9. Provide…

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Q: 47. Let y = sec-x. Show that tan y = vx? – 1 if x > 1 and that tan y = -Vx? – 1 if x 0 on (0, 3)…

A: Consider the function of x and solve further-

Q: Find the limit of sin2x/sin3x as x approaches to 0.   a. 1 b. 1/2 c. 0 d. 2/3

A: here we must know about  L'Hopital's rule to solve the given problem which is used whenever we…

Q: in(cos(x)) 2 limy→0

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Q: In evaluating 4 2 dx X√ X²-4 is same as evaluating lim cos ¹(f(x)). Determine the value of f(x) if…

A: We have to find the value of f(x).

Q: lim-sin t t0 In(2et_1) %3D A © D B.

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Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

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Q: 1 Find Maclaurin polynomial P, to ƒ (x )= 1 1 sin Ax cosx 1-x 1+x

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Q: 1) Evaluate the following limits. cos r - x4 - 1 sin? 2x 3* + cos r a) lim b) lim -00 3+2 – 2* c)…

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Q: d Prove, through the limit process, that (cos x) = - sin x. dx

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