If dr J #(x+1).… (x +n) yields ao In |æ| + aj ln |r + 1| + ... + a, In |r + n| +e where a; (i = 0, 1, ... ,n) and e are real constants, find an. (a) n! (b) п! (c) n! (d) (-1)"+1 ! n! (e) (-1)" – n!

Q: Derive and use the estimate 800 |u (x, t)| < 1 -7²t/10 re (2k + 1)* k=0

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Q: Oz Aradom Variable(x) has the following cof FX(X) = (x³ + x) al find the pdf of X find Pro <xcot)…

A: Given that: The cdf of random variable X is given as: FxX=12X3+X      where 0≤X≤1

Q: 8 f ( x) d( x) =20, f (x) d(x) = – 6, ƒ ind | f(x) dx 2 4 |

A: Find your answer below

Q: 0 eg put (1) in f|L) = < ² cos(21), 3 siu (22), A 3√5 355 255 f(2)= < 3105 |24] 3sin (22) L

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Q: The residue of f(2)=- (A) 1 2011! 1 (B) 2010! (C) 2010! 1 (D) 2009! 2011 at=0 is

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Q: 1 (x² - y²)² x+y valuate: ²₁₁² dx dy

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Q: (4) State which of the following statements are true, vacuously true, or false. (a) (A-B)' = A' -…

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Q: Prove that VÃZ,n,m=N(x²)m = xmn¸

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Q: Which of the following is not true? A Sin(x²)dx= limin(x²)dx c (B) None of the given choices .5 dx ©…

A: Given:  A)∫0elnx2dx=limc→0+∫celnx2dx B) None of the given choices C) ∫05dx25-x2=limc→5-∫0cdx25-x2 D)…

Q: The law of cosines. Prove this generalization of Pythagoras' theorem (see Figure 2.7): || X - Y||² =…

A: As per Bartleby answering guidelines when multiple questions are posted in single picture then the…

Q: In approximating one real root of f (x) = on (1, 3), which endpoint of the interval is constantly…

A:

Q: If lim n→∞ = 1ª + 2ª + + na 1 (n + 1)ª − ¹ ((na + 1) + (na + 2) + + (na + n)) 1 60' (a) 7 (c) -7 ...…

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Q: A = 0 0 0 1 1 1 0 01

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Q: if -2 <x< 0 f(x) dx where f(x) = 4 x2 if 0 < x< 2 -

A: This question is based on definite integral properties.

Q: . Evaluate 6 [₂² (²+2) √₂ (x + 2)√x - 2dr

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 13 - What is derivation of f(x) = (2x2 –x + 1)3 at %3D Xo =1 ? a) O 25 b) 36 030 c) 16 d) 9.

A: What is derivation of f(x) = (2x2 -x+1) 3 at xo =1

Q: 1. Suppose that f f(x) dx = In x + Vx+1+C. Can f be a rational function? Explain.

A: To explain f is a rational function or not.

Q: The interval on which f(x) = 3 – 2x – 12x² – x³ is | - concave down is: O (-4, 0) O (-∞, 4) O (4,…

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Q: Q.2 If f(x) = 2*, Then show that a) f(x+3) – f(x – 1) =f(x) S(x+3) S(x-1) = f(4) b) %3D

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Q: f (x) = { ₂x² (²/²) ² 2=1 Coso f(z) dz= ? 23

A: We have to calculate

Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: 1. Determine the absolute extremum values of f(x) = x? / 2x + 4 on [-3, 1].

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Q: (a) Let a ≥ 2 be a real number. By considering appropriate trapeziums, show that In(a − 1) + In a 2…

A: We have to show that

Q: 3. Find the sum of all values of k such that 2k k -dx =15. (A) 3 (B) 2 (C) 1 (D) 0 (E) 1/2

A: ∫12kx-kx2dx=15∫12kxdx-∫12kkx2dx=15∫12kxdx-k∫12kx-2dx=15x2212k-kx-2+1-2+112k=15x2212k-kx-1-112k=15x22…

Q: Find 2 1² 2 √²+ 3 1³+ f(x, y) dx and f(x, y) dx 3 nd [³ 0 f(x, y) = 3x + 3x²y² = f(x, y) dy = f(x,…

A: We have to find ∫02f(x,y)dx and ∫03f(x,y)dy. If f(x,y)=3x+3x2y2.

Q: Show that ▼ƒ(x) = ["* V²ƒ (x + 7(y − x)) (y − x) dr. - Show all your work pls.(readable…

A: We will use the basic knowledge of integral calculus and vector calculus to answer this question.

Q: (5) Let f(x) = 5x² + for x > 0, where A is a positive constant. Find the smallest A such that f(x) ≥…

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