Let (1x) Prove a) b) = -27 lulx1, 2171 n(n-2) α(n)(x^-2, 14(y)|ds, ƏB(0, E) 1 14 (1)|dy 'B(0, E) И32 n>3 cε||nε), n=2 CE, n> 3 cε ² ||ne|, n=² 2 Cε ², n>3

Q: It is given that 1 (x+3)(x+1) the Fundamental have / 2(x+2) (x+3)²(x+1)² * Theorem of Calculus, we 1…

A: It is given that, 1x+3x+1'=-2x+2x+32x+12. Then, by the Fundamental Theorem of Calculus, we have,…

Q: 15) Suppose that L{f(t)} Then L{-te# f(t)} Corresponds to: a) F'(s – 5) b) –F'(s – 5) c) F'(s)

A: The Laplace transform of the function f(t) is represented as F(s) or Lf(t), it is defined as…

Q: 5y' + xy = x² + 5

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Q: Show that f(r) = O(|x – xo|*) and g(x) = o(]x – roP) imply f. g(x) = o(|x – xo]k+i). - -

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Q: f(x + h) – f(x) f'(x) = lim h-0 %3D h bsnd Diffeentinble A) 7xh2 B) 9x2h C) 5x2 D) 9x2 5) Given (x")…

A: Given that: 4. f(x+h)-f(x)=9x2h+7xh2+5h35. (xα)'=αxα-1

Q: Evaluate L{r'e}. (a-b)! A. aーb+1 (a+b)! В. a+b+1 b! C. (s -n+a) b+1 a! D. (s-b+r)** (ab)! E. ab+1

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Q: 4) The domain of f(x) = 4 cos-(3x- 1) + 5 is 3) If f(x) = 1+ x+x? then f-1(1) = a) 1 d) 2 e) non b)…

A: Since you have posted multiple questions i can do first three questions as per our company…

Q: Find the Taylor polynomials of orders n = 0,1.2,3, and 4 about x = x9, and then find the nth Taylor…

A: f(x)= e ax f0(ln 7)= 7a   f'(x) =ea x af'(ln 7)=ea ln 7 = a 7a   f' ' (x) =ea x a2f' '(ln 7) = ea ln…

Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: 2z Forz> 0, 순(/"m(P + 1) a) In (t³ + 1) dt For x > 0,

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Q: Stan"( 1 -tan m+2 -tan m+1 m+1 1 m+3 Evaluate A B Ⓒ D tan" (x) sec¹x dx. (m + -2)(x) + ¹) (x) - 1)…

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Q: az + b If T(z) cz + d a, b, c, d e R. Show that T(RU{∞}) = RU {∞} if and only if exist

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Q: 15) Suppose that L {f(t)} = F(s) Then L{-te* f(t)} Corresponds to: a) F'(s – 5) b) –F'(s – 5) c)…

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Q: -1-3x+ e3X ) im x>0 hint: L'Hopitals Rule - cos(x)

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Q: 0 (x² - 1) dx b) using the Simpson Rule with n = 6. Show all work!

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Q: Prove that if m is a positive interger, l'(-m+) = 1.3.5..(2m -1)

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Q: Chapter 12, Making Connections, Question 002bi Use the fact that N (t) can be expressed directly in…

A: Use : u(t) = f(t)i + g(t)j + h(t)k u'(t) = f'(t)i + g'(t)j + h'(t)k  u''(t) = f''(t)i + g''(t)j +…

Q: If f(x,y) =log,(cos²(e* )+ sin(x + y) then f(x,y) is ây ôx A) – sin(x + y) B) 0 C) cos (x + y)…

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Q: 71. Find the absolute maxima and minima of the following functions on the given inter G (a) f(x) =…

A: Since you have posted multiple questions i can do first question 71 as per our company guidelines…

Q: (LO16) Find all of the zeros of f (x) = x³ – 4x² + 2x + 4. A) x = 2, x = 1 ± i C) x = 2,x = 1+ V3 B)…

A: If you like the solution then please give it a thumbs up.. The Answer is:       x=2,x=1±3 So, Option…

Q: Vr+2+Vx-2 If a = prove that a -ax +1=0 Vx+2-Vx-2

A: To prove , we need to simplify the left hand side of the equation till it becomes 0. To do this…

Q: 1. Let f(z) = (z+1) (7-3z++2)z and I = P.V. Aiirear . dx. (x²+1)*(x²-3x+2)x If p Res f(z)|z=-i»r =…

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Q: What is y' of y= 7√x 3√x ? A B C D 21√³ (In 7 + ln 3) (In 4) 21√x √x 21√ In 10 2√x 3 In ( - ) 21 V ²…

A: We have to find the point on paraboa y=-x2+4 whose tangent line is parallel with y=3x+5Parallel line…

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

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Q: By using the substitution u = 4x + 1, evaluate (4x+1) dx 1 x²+x+k 4 4x2 + x + k 1 x' + x + k (4x +…

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Q: 3.11. dz, a) y:|z + 2| = 1; (z -1- 3i)(z + 2) 6) 7:|z +1- 2i| = 3;

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Q: 4. a) Solve the equation 5sin-'x- 2n = 2sin-'x-3n 6) Graph, find x where f(x) = g(x), bounded by…

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Q: Find u, v, and ||u + v||. 4, (a) ||ul| (b) |v|| (c) u + v 'T) = A

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Q: Find the arc length (s) of the curve 7(t) = (e*, 4e", - 2et) for 0 <t < In(5) |

A: we are given the curve  r→(t)=e5t,-4e5t,-2e5t =e5ti-4e5tj-2e5tkwhere 0≤t≤ln5

Q: 4. Evaluate [(3x? - x + 6)dx i) 1 + 1(1? +1)' ]dt ii) o V1 +x* iii)

A: 4 (i). Given integration is : ∫-133x2-x+6dx To find the value of integration.

Q: If S., t, = \n(n+1)(n + 2)

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Q: Evaluate 4xe dx in terms of erf(x) A) 뜰[1-erf(-4) B) V#[1- erf(4))] C) V (erf(4) – 1)) D) ferf(- 4)…

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Q: D (1) √².dx = √√x²-4x x-2 +CD) In√2+ -4x cond derivative is continuous on [-1, 1]. Then [xf"(x), dr…

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Q: Let x, y = {0, 1}" and let s = xy. Show 1 Hon • (2x) + √2)=√√ Σ (-1)ײ |z) z={s}+ 2n-

A: The Hadamard transform is a quantum gate that is commonly used in quantum algorithms and circuits.…